They do, it's just that many choose the reverse charge mechanism, so the recipient of the services or goods is responsible for paying the VAT to his tax authority. It makes things easier, it doesn't remove VAT.
For almost all B2B cross-border transactions between two VAT registered entities, the reverse charge is mandatory, not something that you can choose to opt in to.
Are you sure? If a software company pay it's contributor dinners in Bruxelles/Milan/Lisbon, is the reverse charge mandatory too? Because it seemed like business as usual each time I went on business trip.
In practice, when you buy something with VAT reverse charged, you normally declare the VAT to be paid and immediately claim it back on the same declaration. So in the net you pay nothing, but the VAT is of course still there.
