How is this different from having to account for different state and local taxes when selling software inside the US?
With VAT, you have to keep careful track of input VAT and sometimes later claim repayment from various governments.
There is a lot of obligatory registration and document submission.
The velocity of legislative change is high, especially when summed across member states.
Small entities have an incentive to underreport. Thus, a lot of enforcement activity is targeted at small entities.