I found service in restaurants in Europe to be notably slower than in the US.

I didn't think it was about tipping–if most tips are in the same narrow band (15-20%), that doesn't explain much difference in speed.

But the existence of tips–even with a narrow band–incentivizes turning as many tables as possible.

So even if the average "salary" comes out the same with the default tipping rate, the one with tipping will incentivize faster table service than the one without tips, which doesn't reward based on how many tables were finished.