For sales to be "local", products need to be stored in warehouses in each country. But that in turn means the owner of said products (the seller) has to be registered for VAT in that country, and submitting annual reports in each country's language.
I went to the trouble of registering in 6 different countries; in some countries, Amazon more or less helps sellers submit reports; in others, they offer to partner with local lawyers.
The result is a mess of reports, injunctions, penalties for late filing, etc. coming to you in Polish, German, Spanish, Hungarian. I eventually gave up.
Europe is not actually a "single market". It's a federated bureaucracy entirely indifferent (or hostile) to small businesses.