Not speaking from experience, but our local family surgery does them on the premises under a local. To have a general means booking in to day surgery, waiting around half the day for your turn etc etc.

DH has said he would rather a general, but I have the same concerns as OP about using them willy-nilly, when a local will suffice.

I had a LLETZ procedure (abnormal cells removed from my cervix) done under a local, and it was no problem, so DH should be able to have a V done under a local too