It depends on the damage. Is the bezel broken/cracked? Is the lid broken? or just the hinge mounting holes? If the technician really knows what he/she is doing and can deliver a result like it never happened, then yes it can be expensive, as laptop lid+bezel+hinges disassembly/assembly and repair require precision and experience.

I had a similar problem with my A315 (the hinge mounting holes on one side got smashed, but bezel and lid were OK), attempted to repair with epoxy putty, did not hold, searched Aliexpress and luckily found the exact original lid (but now I also need a new bezel because I damaged its clips during disassembly and reassembly).

I'd suggest you check Aliexpress, order the lid+bezel if you can find just the right parts (should not cost more than USD 75) and then go to the service with them. You might get a better service fee in that case.