Tariffs on services may also be less popular with the citizens. It's not obvious that the locally produced fridge is only cheaper because of tariffs. It will be more obvious that everyone non-EU based pays more. It will also be harder to control (how will EU extract tariffs for payments I do to companies with no EU presence?)

But I don't how much about it, maybe these are already solved problems. After all VAT already exists and faces similar challenges.