Most likely the government will find a way to control cryptocurrencies transactions, that's what they start to do in China, that's going to happen all around the world soon. At the country where I live now (Vietnam) they are planning to make BTC an official payment method for governmental services - I'm sure that one of the ways they want to get taxes from citizens
Are you sure of that?
Since if you are and the government is really going to accept Bitcoin as a means of payment for public services, that basically means that you can pay taxes in Bitcoin directly. Taxes (as you yourself imply) by their very nature are the payment for such services (i.e. "the source of money to keep infrastructure growing"), and paying taxes in some token effectively makes this token into a legal tender since the definition of legal tender is exactly that, i.e. a means of payment for all public debts, taxes, and duties
The only way governments would be able to tax Bitcoin is if they do what you just said - require payment in Bitcoin directly. Otherwise good luck trying any other method.
And someone just proposed they tax exchanges. In my view this is actually the best option that governments have at this point as they can track each person's trades and tax based on that. Everyone would need to upload their IDs and such and have one account only per person
This won't work out for obvious reasons
And it is not just about taxing Bitcoin specifically or Bitcoin exchanges in general. Ultimately, it is about taxing everything (mostly the profits of companies and corporations), and this is where tax havens and offshores massively kick in and effectively destroy all such efforts on the government part. In other words, the "methodology" of rendering government interference futile, null and void is already there, has been there for decades, and is pretty polished and robust as well as efficient and effective