I got Plumbing Merit Badge over 40 years ago. I don’t recall facing a stuck single handle valve.
While trying to fix the balky handle on our Moen Adler Centerset Single-Handle Bathroom Faucet, I broke the stub on the water control valve that’s connected to the handle. Mineral deposits from our water had built up inside the handle, effectively welding the plastic to the brass.
We weren’t so hot on the design of this particular faucet, so instead of replacing the valve, we decided to replace the entire faucet.
We opted for the high tech American Standard Monterrey Centerset Gooseneck Lavatory Faucet with paddle handles for keeping our hands clean when we wash up for surgery. I jury rigged a screw and a piece of wood for a handle for the old faucet while we waited for the delivery of the new faucet.