First, contra to your last statement, deflation is obviously harmful if one considers its effect on growth via demand:
The nominal interest rate cannot fall below zero, because that would mean reducing savers’ bank balances every month, and would prompt them to withdraw their deposits from banks and stash cash under the bed. Together with inflation, this puts a floor on the real interest rate too. If inflation is low and real rates can’t fall far enough to boost demand and perk up prices, demand will weaken still further. This is the dreaded deflation trap.
What you're missing from your model is any notion of savings and interest. There's also the psychological issue of cutting wages in nominal terms to keep up with deflation. (As an aside, that's also one of the reasons why laying off people is preferred to wage cuts in a downturn.) I'm sure there are more questions here on econ.SE about deflation.
Second, the real answer to your question (targeting a non-zero inflation) is price stability. To quote your an ECB paper:
We are interested in finding the price index [i.e. inflation] that, if kept on an assigned target, would lead to the
greatest stability in economic activity. This concept might be called the stability price index.
Constructing the latter is pretty complicated in a multi-sectoral model, and you're invited to read ECB's paper. But avoiding deflation is one of the goals:
Inflation rates of below, but close to, 2% are low enough for the economy to fully reap the benefits of price stability. This aim also underlines the ECB’s commitment to provide an adequate margin to reduce the risks of deflation. Having such a safety margin against deflation is important because there are limits to how far interest rates can be cut. In a deflationary environment monetary policy may thus not be able to sufficiently stimulate aggregate demand by using its interest rate instrument. This makes it more difficult for monetary policy to fight deflation than to fight inflation.
As for why some arbitrary number >>0 for inflation decreases economic stability... that is slightly more involved to answer in modelling terms, I won't attempt that here. A highly cited empirical paper by Barro (1995) found that when high-inflation is included in the sample growth is negatively affected:
Data for around 100 countries from 1960 to 1990 are used to assess the effects of inflation on economic performance. If a number of country characteristics are held constant, then regression results indicate that the impact effects from an increase in average inflation by 10 percentage points per year are a reduction of the growth rate of real per capita GDP by 0.2-0.3 percentage points per year and a decrease in the ratio of investment to GDP by 0.4-0.6 percentage points. Since the statistical procedures use plausible instruments for inflation, there is some reason to believe that these relations reflect causal influences from inflation to growth and investment. However, statistically significant results emerge only when high- inflation experiences are included in the sample. Although the adverse influence of inflation on growth looks small, the long-term effects on standards of living are substantial. For example, a shift in monetary policy that raises the long-term average inflation rate by 10 percentage points per year is estimated to lower the level of real GDP after 30 years by 4-7%, more than enough to justify a strong interest in price stability.
Another observed fact from high[er]-inflation periods that has some explantory power is that higher inflation reduces the performance distinction between stocks and bonds (thus lowering the attraction to invest in more growth-producing assets):
By contrast, when inflation is higher and more volatile—
as it was in the 1970s [US] —the correlation between stocks
and bonds increases. Because rising inflation negatively
affects the performance of both stocks and bonds,
bonds generally become more equity-like amid higher
inflation and thus tend to provide less diversification.
In theory one might be able to come up with a model where high but stable inflation exists (you actually did that), which might cause stocks and bonds to behave differently [enough], but in practice such historical examples of high but non-volatile inflation are rather lacking.
The textbook problems with high level of inflation (not taking volatility into account):
- "shoe-leather" cost: keeping lower money balances when inflation is high (implying more frequent trips to the bank/ATM).
- menu cost: time and effort to change price lists in an inflationary environment
I'm not sure how well-tested these are in practice (as distinct effects).
On top of those level effects (which are disputed by some economists), volatility in inflation brings its own problems:
E.g. an ECB paper stating these as well-known facts:
Among the harmful effects of inflation, the negative consequences of inflation volatility are of
particular concern. These include higher risk premia, hedging costs and unforeseen redistribution of
Or another empirical paper actually evaluating the effect of inflation volatility (separately from level):
This paper re‐examines the relationship between inflation, inflation volatility and growth, using cross‐country panel data for the past 30 years. With regard to the level of inflation, we find that exploiting the time dimension of the data reveals a strong negative correlation between inflation and income growth for all but low inflation countries. To examine the role of inflation uncertainty on growth, we use intra‐year inflation data to construct an annual measure of inflation volatility. Using this measure, we find that inflation volatility is also robustly negatively correlated with growth, even after the effect of the level of inflation is controlled for.
As far as I know far fewer economists disagree with the latter points, i.e. that volatility of inflation is bad (for growth). E.g.:
While the level of inflation was found not to have a significant effect on growth, [...] inflation volatility does significantly impact growth even for countries with moderately high levels on inflation.
There are also works that discuss whether/why inflation uncertainty rises with the inflation level, i.e. even if you don't have actual volatiliy of inflation, a perception of an increased risk of volatiliy may be enough to create negative effects associated with volatility.
While the costs of inflation uncertainty are
relatively easy to identify, explaining why inflation
uncertainty increases with inflation is more difficult.
The most appealing explanation involves the
response of monetary policy to inflation.
inflation is low, monetary policymakers try to keep
it low. To the extent they are successful, inflation
remains low and stable. When inflation is high,
however, monetary policymakers are more likely to
adopt disinflationary policies. These policies, by
lowering the inflation rate, increase inflation variability.
Moreover, the policies create inflation
uncertainty because the timing and short-run impact
of policy on inflation are uncertain.
Basically it is a learned effect from what central banks usually do.