Botcoins are not anonymous at all when you buy them with fiat currency unless you take additional steps to make them hard to trace (but still not anonymous). Years ago I traded in cryptos and "luckily" I sold my 1.5 BTC at the historic high price of ~$1400. It should never go that high again, so right now I'm without a single satoshi and I have to buy. I do not remember that I had to submit my IDs to exchanges back in the day, nor having to wave in front of a camera.
As for the e-mail provider, I tried that one, I think it requires payment or a referral code. This is really starting to get on my nerves, I just want to donate to this website and (no fault of the website admins of course) I am unable to just buy some BTC.