I am a Mason and build fireplaces if I have to and repair them and chimneys as well. A fireplace is a waste of firewood,nice ambience,but that's it. 10 to 15% efficiency doesn't even deserve the term efficiency.
You can get a lot of work done for that amount of money. My guess is the guy is very busy and throws out high numbers in hopes a few will bite. You do not have to bring a fireplace up to code,at least not here in NY.
It takes a lot for a fireplace to fail. The smoke chamber takes the most heat, so I could see it being corroded. He said the flues are ok,that is a good thing,I see lots of cracked ones.
I also recommend getting another price or two if you can. Even if you have to pay for the estimate,it is worth it.
The guy is not wrong about being extra cautious either,playing with fire can kill you.
Do you have a working damper in the fireplace? if not I would go for the rooftop damper,that will save on your heating bills. One of those should cost around $500 installed.