There are people who specialize in sales between EU states, but for a small team without capital it was hard. That said most of the 100+ tech companies I know of have offices around EU to get talent from other countries.
Bank payments are easy yes, but credit cards are not ubiquitous, online payments are different in all countries, direct debit is not always supported across countries.
So for businesses expanding into new EU countries it's not as onerous as needing a local presence would be.
(Disclaimer: I'm not an accountant and may be wrong. I'll take it on the chin if so. This is just my understanding, having needed to look this stuff up occasionally.)
[1] https://europa.eu/youreurope/business/taxation/vat/cross-bor...
[2] https://europa.eu/youreurope/business/taxation/vat/cross-bor...
[3] https://europa.eu/youreurope/business/taxation/vat/vat-digit...
[4] https://europa.eu/youreurope/business/taxation/vat/cross-bor...
Alza (CZ) is slightly bigger than a medium sized online shop and they are using CZ VAT ID intentionally for intracomunitary B2B sales, even though they do have physical presence in other countries.