Most of the time it's not too bad to appeal a claim for smaller amounts. People go through the hoops for the larger denials because they are so motivated.

I got a $150k bill for emergency care for my daughter once; it wasn't too bad because they denied it as "uncovered elective procedure" which was trivial to show it wasn't, but it was still a tense month for me waiting. The punchline, of course, is that the insurance company and the provider agreed upon $30k.

Doctors' offices can't tell you what a procedure will cost ahead of time, and the amount they bill you afterwards is completely fictitious (because if you don't have health insurance you probably can't pay 5x what the insurance companies pay, so will be bankrupted anyways).