How else do you prove that the serial number of every part fitted matches the log book except by a huge inspection.
You don't have to. The aircraft has a valid CofA, the last engineer to inspect and give it a CofA is certifying to the aircraft has been maintained correctly and that all AD's etc have been complied with. Under Part M they are only required to go back to the last CofA to ensure any work or parts applied is compliant.
Hence the comments here and in other place about the 'interpretation' that some maintenance companies are putting into the rules.
Some I have talked to are interpreting the rules in the correct manner, others are not and some are just using it as an opportunity to drop peoples trousers.