I thought there was an official governmental point of contact that handled such complaints, and had teeth?
The Data Protection Authority are underfunded and understaffed. They try the best with their resources.
Not the best way, I know, but better than nothing.
Police enforcement includes the police powers of arrest and detention.
GDPR enforcement is (I believe) limited to a fine which can be appealed to a court. If the enforcement department turns out to be wasting court time, then there are likely to be significantly negative consequences for that department (at least, more than for the police in the US).
I agree that fine collection is not an ideal way of funding a department, but not all incentives are perverse just because they exist - incentives are allowed to align.