Well yes and no. In most places (around here in Europe at least) whenever you visit a café or restaurant, you'll be served a café crema, tapped out of an espressomachine, which is considered to be more luxurious, but not served by starbucks. Drip brew is usually served wherever coffee is free of charge like some work places or cantines. So after serving drip brew as a normal coffee, you'll find lots of unemptied cups all around the cafe when doing your bussing routine.

So yes it might come across as annoying but a bigger chance of satisfaction for the customer.