Petty homeowner renovation stuff is basically a weird tax in disguise. They don't care, they were never gonna tell you no. They just want your money and want you to make work for whatever trade is being made work for in the process.
Go for a variance and then see how you feel about it. Better yet, go try and create any sort of occupied structure or commercial use where one doesn't already exist.
Local permitting is riddled with bike shedding, people trying to avoid responsibility, people trying to advance their pet interests at other people's cost and probably more stuff I'm forgetting. At least with state level stuff you can be all "I've paid my engineer big bucks, here's there work output, here's why it's GTG, and if it is in fact GTG they typically rubber stamp it. But little guys can't afford to play in that arena unfortunately.