One has nothing to do with the other, ever. Yeah, it sucks but again, they do not trigger each other. Event "A" doesn't lead to Event "B".
If you want out, sounds like this is the time to get out before you are asked to sign off on your inspection contingencies. If you didn't pay for an appraisal but they orderred it, I wouldn't pay even if they asked. I'm confident they'll push you to pay for it but as confident that if you dig your feet it, the lender will eat the appraisal fee.
No, they shouldn't have waited for the home inspection though to be finished. Also, you never order the appraisal. The lender always does.