When trading between EU countries, although you have to calculate and charge VAT based on the location of your consumer customers, if your business only does a small amount[1] of goods trade with various EU countries, or if it's supplying services[2], or if it's supplying online services[3], or if it's supplying goods or services to other businesses[4], it isn't necessary to have a company presence in each individual country.
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...
I do not see these things as a big problem though, payments are is a service we buy for our own country as well. The same service provider doesn't work everywhere but for us that is not a problem.
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.