Inspections if any would be on the electrical and plumbing fixtures. There is no such thing as cabinet inspections. If you are replacing at existing locations and not changing rough ins and you are handy you can do without. The fact they didn't tell you they were removing old fixtures means that's on you. If you don't pull permits do yourself a favor and don't order a dumpster to be delivered. Dumpster with old cabinets in it would be calling card for town to ask questions. Either yourself and a buddy do it on weekend and get it into a truck and off-site ASAP. Or ask cabient supplier for a quote to gut and remove. They may or may not do plumbing and electrical disconnect "in house". If you are not handy and or moving fixture locations, permits and inspections are in place to protect the homeowner from dangerous or shoddy workmanship.
