BATFE can inspect the business premises of an FFL 01 dealer to ensure that all the guns on the premises are properly recorded or are exempt for some reason (e.g., personal property of the dealer). The justification is the need to ensure proper record keeping and that a dealer is not buying and selling "off the book", or "leaking" inventory through illegal sales, carelessness, or theft. That, IMHO, is a very good reason NOT to have business premises in the home or at least to keep the business area separate from the living area. Otherwise, the "sock drawer" could be subject to inspection if the dealer keeps part of his inventory in his bedroom. (Yes, I know dealers who do just that!)
That is not the case with a C&R FFL. Since it is presumed that the C&R licensee has no "business premises" (for his collecting activity) and that he carries out that activity in his home, BATFE is limited to inspecting his book and if the licensee chooses that can be done at the BATFE office, not at the collector's home. But even for a C&R FFL, if there is cause to believe there is some illegal activity, like illegal dealing, a warrant can be obtained to search the house.