It's rare for parents to ask me to sing the Birthday song too, but it happened often enough for me to decide to make it a part of my Birthday party package. Truth is, if I don't lead the Birthday Song, it can be a really flat moment; often no one will really sing out, and it can feel like a real anti-climax. Of course, it's up to each individual entertainer to decide if he's comfortable leading the singing. But realistically, a performer is likely to make more of the ceremony than the majority of parents.
As I've mentioned here before, I only offer a full 2 hour party package for Birthdays, which maximises my income. I only work 2 parties a day maximum.

I've never been asked to serve the cake.