We have guested both ways - paying and non-paying. The only thing that I can say about paying is that it is a little easier with the other parents when your DD plays a lot of innings and you are paying just like everyone else...
Exactly. If your DD is invited to play, make sure that you know exactly what the expectation is for playing time before you commit. It would be nice if the coach communicated that to the other parents too but unfortunately that doesn't happen very often...
Usually I have a discussion about what they need. If my DD is going to be a sub and a just in case player cause they want to play their girls, then I don't expect to pay. If she is going to be at third all weekend, then I'll insist on paying.
My DD's a pitcher so when she's picked up it's mostly been for that. She's a beast in the field though and usually ends up playing more than expected rather than less (we have not had issues with parents over it, fortunately - she has not picked up in almost 2 years though). I'm OK with paying or not paying. If it's covered, great. If not, I can chip in. We play because she wants to, it's not a big deal to contribute. We've only been asked to once.