Here’s the context. I want to know what the theoretical market capitalisation (say eg $US / Bitcoin times Q the number of coins - it doesn’t have to be Bitcoin) of a crypto currency? Assume that the crypto currency is uniformly better than fiat. I think it tends to infinity. To see this, let’s say everyone decides that a digital currency is better (eg because you could avoid tax / minimise transaction costs), then in an extreme scenario ppl decide that it’s just better to hold digital currency rather than fiat - so demand for fiat currency in that case tends to 0 and exchange rate between fiat / digital currency tends towards infinity because the fiat becomes worthless. So it’s kind of like holding a stock that’s price goes to 0. And that probably explains the considerable growth of digital market capitalisation. Is my reasoning correct?
Unfortunately, those who are riding the current trend do not have a clue about what they are doing. I guess, they don't even think of hypothetical situations you've given above to legitimise cryptocurrencies, instead, they appear to be enjoying the joyride. If anything, cryptocurrency trading is more like a fantasy share trading with real consequences.
As of now, there are 1354 cryptocurrencies.
As you suggest, "investors" may have decided that digital currencies are better "(eg because you could avoid tax / minimise transaction costs)".
As there is no practical limit on the number of cryptocurrencies that can be created, and as no one crpytocurrency has a unique advantage over any other, and as no cryptocurrencies are legal tender anywhere, the theoretical market cap of any one cryptocurrency has zero underlying value.
What its actual market cap is, will depend on how many suckers can be lured into purchasing it, and what their combined purchasing power is.
Furthermore, even if all your incorrect assumptions were correct, your conclusion would not be: the total capitalisation of all existing sovereign currencies is finite. If they were all to be replaced by a cryptocurrency, then its capitalisation would be much less than the existing total capitalisation of all sovereign currencies, because economic activity would have taken a huge downturn. That's because the world is not an Optimal Currency Area.
This is not to say that cryptocurrencies will never have any value. But at time of writing, there is no visible legitimate application that gives them value.
You can measure capitalization if a "crypto currency" is a security (an investment asset). For currencies, you can measure the money supply - the total amount of currency available. You are trying to measure the total money supply in a foreign currency. For this you can multiply the total money supply by the exchange rate, as you already suggested in the question.
The main issue with crypto currencies is that they are being bought and traded as securities rather than currency.
Definition of security (USA)
(...)a contract, transaction or scheme whereby a person invests his money in a common enterprise1 and is led to expect profits solely from the efforts of the promoter or a third party.