Although getting a C&R does give the BATF permission to inspect your bound book and collection, it's limited to once/year max, and must be during reasonable hours. If you don't want to let them into your house, you can arrange to do it at their offices. Also, the inspection only applies to firearms that you've acquired/disposed of that are qualified as C&R and are listed in your bound book.
Getting the C&R doesn't give up any freedoms - that was done years ago in the GCA of 1968. It swaps one little bit of freedom for another - you gain the ability to have a particular class of firearms shipped directly to you, while granting the government permission to inspect your records concerning those firearms. Is it worth it? That's up to you. Me, I think it is - I've got a C&R, and so far haven't been inspected (about half-way through the 3-year license duration).