Is the only benefit to fluctuating currency rates that it means some people make a lot of money by trading currencies, with zero appreciable benefit to humanity at large ?
No. The main benefit of flexible exchange rates is that it allows the currencies to adjust to imbalances in the balance of payments between countries, itself a result of real economic differences:
An upwards shift in the value of a nation's currency relative to others will make a nation's exports less competitive and make imports cheaper and so will tend to correct a current account surplus. It also tends to make investment flows into the capital account less attractive so will help with a surplus there too. Conversely a downward shift in the value of a nation's currency makes it more expensive for its citizens to buy imports and increases the competitiveness of their exports, thus helping to correct a deficit (though the solution often doesn't have a positive impact immediately due to the Marshall–Lerner condition). [...]
When a country is importing more than it exports, the supply of its own currency on the international market tends to increase as it tries to exchange it for foreign currency to pay for its imports, and this extra supply tends to cause the price to fall. BoP effects are not the only market influence on exchange rates however, they are also influenced by differences in national interest rates and by speculation.
Some economists think that some level of buffering by the central banks of exchange rates is necessary though, because exchange rates are vulnerable to speculative because they tend to converge too slowly to their "real" value. (The latter is sometimes called the PPP puzzle.)
When central banks work to affect the exchange rate without changing the money supply, it' called a "sterilized intervention". It's somewhat controversial whether these work as intended or not.
Also, a pegged system largely exports one country's (the biggest one, economically) monetary policy to the rest. This causes substantial problems if these other economies are dissimilar.
This implicit export of monetary policy via (nearly) fixed exchange rates is thought to be a key reason why the Bretton Woods system (which nearly achieved what you ask for), eventually failed:
Increasing US monetary growth led to rising inflation, which spread to the rest of the world through growing US balance of payments deficits. This led to growing balance of payments surpluses in Germany and other countries. The German monetary authorities (and other surplus countries) attempted to sterilise the inflows but were eventually unsuccessful, leading to growing inflationary pressure (Darby et al. 1983). [...]
The decision to suspend gold convertibility by President Richard Nixon on 15 August 1971 was triggered by French and British intentions to convert dollars into gold in early August. The US decision to suspend gold convertibility ended a key aspect of the Bretton Woods system. The remaining part of the System, the adjustable peg disappeared by March 1973.
A key reason for Bretton Woods’ collapse was the inflationary monetary policy that was inappropriate for the key currency country of the system. The Bretton Woods system was based on rules, the most important of which was to follow monetary and fiscal policies consistent with the official peg. The US violated this rule after 1965 (Bordo 1993).
N.B. The Bretton Woods minus the gold standard, thus only a nearly fixed exchanged system (but not backed by gold) is sometimes called the Smithsonian Agreement. It lasted between 1971-1973. Without a change in US monetary policy (which didn't really happen) it couldn't have possibly worked:
At the Smithsonian meeting, the United States agreed to devalue the dollar against gold by approximately 8.5 percent to $38 per ounce. Other countries offered to revalue their currencies relative to the dollar. The net effect was roughly a 10.7 percent average devaluation of the dollar against the other key currencies (de Vries 1976, 555).
At the Smithsonian meeting, countries also agreed to future talks on broader reforms of the international monetary system. Issues that would be discussed included the central role of the dollar, shared responsibility for exchange-rate stability, the future role of gold, a means for easing exchange-rate adjustment, and measures to deal with volatile financial flows. Foreign nations also agreed to comply with Nixon’s request to lessen existing trade restrictions and to assume a greater share of the military burden.
The Smithsonian Agreement did little to restore confidence in the Bretton Woods system. During 1972, speculators pushed many European currencies toward the tops of their permissible—but now wider—exchange-rate bands. By intervening, their central banks accumulated large amounts of unwanted dollars, which stoked inflationary pressures. Germany and Japan expanded their restraints on financial flows, and other countries began to follow suit.
Gold prices, a barometer of uncertainty, rose to around \$60 an ounce by mid-1972 and $90 an ounce by early 1973. Speculation was rife. On February 12, 1973, with exchange markets in Europe and Japan closed, the United States devalued the dollar by an additional 10 percent to \$42 an ounce. When markets reopened, speculation against the dollar became rampant. Within a month nearly all major currencies were floating against the dollar. The Bretton Woods system was finished (IMF 1973, 2-8).
As you can see, (nearly) fixed exchange rates encourage rather then discourage
speculation, when there is an imbalance of payments.
Now if you want to talk about erasing different currencies altogether, the imbalance of payments problem doesn't disappear but becomes a "persistent imbalance" in development, taking the EU as an example:
As a monetary union based on a single currency, the Eurozone was supposed to be immune from these problems, as exchange-rate risks would vanish and payment disequilibria within the area would be smoothly offset by private capital flows (James 2012). These expectations proved delusional; the sovereign debt crisis in the Eurozone in 2010-12 started as a fully-fledged balance-of-payments crisis (Baldwin et al. 2015), prompted by the accumulation of large payment imbalances between its members and reflecting persistent underlying divergences in prices and costs. [...]
In sum, Germany has emerged as a kind of real economic anchor of the Eurozone, forcing its preference for high savings and slow growth of domestic demand onto the other members. However, this slow growth is incompatible with the need to reduce debt and reabsorb much higher unemployment and social distress. At the same time, very low inflation further compresses the margin for change in relative prices and wages.
And if the Eurozone (EZ) crisis needs more explaining, from Baldwin et al.:
The core reality behind virtually every crisis is the
rapid unwinding of economic imbalances. In the
case of the EZ Crisis, the imbalances were extremely
unoriginal – too much public and private debt
borrowed from abroad. From the euro’s launch till
the Crisis, there were big capital flows from EZ core
nations like Germany, France, and the Netherland
to EZ periphery nations like Ireland, Portugal,
Spain and Greece. [...]
All the nations stricken by the Crisis
were running current account deficits. None of
those running current account surpluses were hit.
When the EZ Crisis started, there was a ‘sudden stop’
in cross-border lending. Investors became reluctant
to lend – especially to banks and governments in
other nations. The special features of a monetary
union meant that the ‘sudden stop’ was not
precipitous (as it was, for example, in Iceland).
Rather this ‘sudden stop with monetary-union
characteristics’ showed up in rising risk premiums.
The abrupt end of capital flows raised concerns
about the viability of banks and governments in
nations dependent on foreign lending, i.e. those
running current account deficits.
(If you care about Nobel lustre, Pissarides is one of the co-authors of that last paper.)
Finally, Gros and Alcidi discuss the finer differences between a hard peg (fixed exchange) and a monetary union in fairly similar economic circumstances... with a naturalistic example for the former: the BELL countries, i.e. Bulgaria, Estonia, Latvia and Lithuania (which had or have a hard peg to the Euro while not being part of the Eurozone--actually Estonia joined the Eurozone in the period under investigation). It's a little too detailed to get into that here. But as a general idea:
From a macroeconomic point of view, there should be little difference between a monetary union and a hard peg (e.g. a currency board). There is no national monetary policy autonomy in either case and the constraint on fiscal or budgetary policy should also be essentially the same in the long run.
In fact, however, one difference still exists. In the case of a currency board, the country can break its
commitment to keep the exchange rate fixed without causing any problems for the country to whom the currency had been pegged (the collapse of the peg of the Argentine peso to the US dollar had no impact on the
confidence in the dollar). However, in the case of the euro, the exit of any country would have a profound
impact on the other member states of the currency area.
The latter event is hypothetical as we have no historical examples as far the Euro goes, but there certainly has been no shortage of opinions on the matter.