Estonia, Greece and Cyprus use the Euro, but unlike the other EU Euro countries aren't available on Stripe.
I haven't worked in finance, but as I understand it, the regulations are supposed to allow cross border businesses to operate. That's why the City of London banks area worried about leaving the EU and losing that right. The Eurozone especially has regulations to remove barriers to cross border payments.
The EU makes it easier for more businesses to operate across borders, but banks and payment companies are still highly regulated on a per-country basis, with few real standards for having regulators talk to each other.
The main downside of not being in the EU is that it'd be harder for the banks' clients to move money to the EU, likely trigger additional taxes, etc.
There's a conspiracy theory that they're actively not rolling out to Estonia because the e-residency feature makes for a possible interesting competitor to Stripe Atlas.
I haven't worked in finance, but as I understand it, the regulations are supposed to allow cross border businesses to operate. That's why the City of London banks area worried about leaving the EU and losing that right. The Eurozone especially has regulations to remove barriers to cross border payments.
https://www.paymill.com/ says it works for all of the EU except Cyprus. Perhaps an oversight?
This might be of interest: https://en.wikipedia.org/wiki/Single_Euro_Payments_Area