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You just ask for the user's location. A dropdown box with countries.

That's not unusual, American companies do that, too, in order to calculate sales tax.

You probably need it anyway to calculate shipping.

Most Europen countries also have their own languages. All of them have their own top level domains. And despite the Euro, there are 11 different currencies used in the EU.

VAT just isn’t particularly hard, as business problems go.

It's not that trivial either (search for "VAT MOSS" to learn more), but otherwise your point is valid.

you just display the price with your local VAT. In the last step, if the user is from a different country AND if you do more than 100k eur revenue for that country/year, you recalculate with the correct user VAT.

And if you are Amazon, you then give the diff as a discount if it was more than advertised.