I don't think cutting a small hole in between studs requires "architectural design" and "electric load calculations" really means "it uses this many watts". There is nothing typical about someone needing a year to do something relatively simple. Most restrictions probably just say that the condenser coils can't be on the side that faces a street and maybe that it has to be on a dedicated circuit.

You would think, but California is a weird world where often it does take that long.

Both of your comments are basically saying 'this is true' and saying 'this is true' again. Do you have any sources or even reasons why installing a split unit air conditioner in all of california 'often' takes a year?