The solution was to replace the compressor so the compressor must have been the only problem.

If the A/C guy had to replace something else and the compressor, there might be a chance a smaller breaker could have saved the compressor if the "something else" might have caused the compressor to stall. If the something else just caused the compressor to overload, its internal overload protection should have handled that. Breakers don't protect against overload.

The A/C guy said the reason the compressor failed is that the breaker was too big, I have to wonder what motivated that. I don't think that idea will fly.

Sometimes compressors fail.

Still the breaker should be properly sized to protect the conductors. You might be able to stick the electrician with that cost. He relied on the guy before him to properly size the breaker. Maybe you can get the original installer to pay for the breaker.