Most EMIs don't do USD because it's just too much trouble for them. It's actually a problem for regular banks as well, even big banks can just lose a correspondent bank and lose the ability to do USD transfers for months...
A regular bank inside of the IBAN system will open you an USD account without problem (note that IBAN system countries are larger than SEPA countries and those are in turn larger then Eurozone countries).
And even then, when you have an USD account inside of the Eurozone, it doesn't help you much. Euro (SEPA) payment? Easy, sometimes can be even received instantly within minutes across two different countries. USD payment (wire)? Prepare to wait 2-3 days or even more, prepare to provide recepient's detailed address and even then it may be blocked.
I heard from a friend that he was sending money in USD from
Germany to Russia. This payment was blocked by the US because the recepient's name was similar/identical to some Russian guy on some blacklist. So imagine that, you are sending money from country A to country B and United States intervene because they don't like that!
I hope this system of USD reserve currency and correspondent banks dies and something like
crypto replaces it.