I strongly disagree with that notion. Even if you know in advance who will be profitable, you often gain more customers by servicing all customers (or at least the vast majority).
Two examples:
1. A lot of internet companies are built on servicing everyone, and extracting money from a tiny subset (github is one example).
2. If one in every thousand customers costs me more in support than they pay, that's one thing. But becoming known for good support will be more profitable than becoming known for kicking customers who ask too many questions.
The cost for support is low too, relatively speaking. Obviously not all businesses have enough margin to consider this, some support is more expensive than others etc.
The problem is when you accept customers and then don't provide proper service.
They could require $1k or $10k per month minimum volume. But they don't. They accept everyone and then stonewall at random, sometimes even when people are high-volume.