Even undocumented immigrants citizens pay taxes because its deducted from their income before payment how much more a citizen who is well documented. [...]
Are we still talking EU? EU employers will automatically deduct your taxes, that is correct, but as far as I know they can only do so with registered employees that have a working permit.
Wait. What you're saying is that if I withdraw a portion of bitcoins (I myself don't own any) in Europe, I'd be taxed on them even if I held them for over 1 year, but bought them in another country originally? Or do I pay the tax in the country I now reside in, even though I just moved a few months ago? [...]
1) Taxes on Bitcoin sales do not get automatically deducted in any European country, you will have to file tax reports yourself.
2) Taxes vary
wildly between EU member states. Not just in regards to crypto. Be aware that the tax-free-after-1-year-of-holding rule only applies to a handful of countries (eg. Germany, Austria,... not sure where else). Selling before the 1 year holding is usually taxable as income tax (which also varies wildly between member states), selling after the holding period is usually taxable as capital gains tax (or not at all, if you're lucky). Either way, look closely into how each country handles taxation.
3) In which country you bought the Bitcoin originally doesn't matter. You should be able to prove holding time though. Arguably referring to the blockchain may suffice, but as far as I know there has been no precedence on how to report holding time correctly so far -- and you can also expect that what counts as proof for holding time will vary wildly between EU member states.
4) You pay tax in the country you reside in, assuming you have already taken full residency and have become a tax resident. At which point you become a tax resident depends on the country you move to and likely also where you are originally emigrating from (ie. immigrants from non-EU member states have to follow different rules than immigrants from EU member states. I wouldn't be surprised if there's a set of rules specifically for immigrants from the US). Prepare for paperwork as you likely won't become a tax resident automatically, but also will need to become a tax resident at one point to be allowed to legally stay there for a prolonged period of time -- assuming you don't have citizenship already.