Or you could let them cool down while you eat, then fill them with water. Soak for 15 minutes and the food wipes right out with a plastic scratchy pad.
Twice a year I polish them with Barkeepers Friend. I don't have to, but wow do they look great.
Or you could deglaze the pan while it’s hot and turn the stuck on stuff into a sauce. That’s the French way to avoid scrubbing your pans.
Bar Keepers is great stuff. I just hold the hot skillet or sauce pan under a dribbling kitchen faucet and with a wooden spoon for a scraper, it comes amazingly clean - but yes, your way works great to for pans that have cooled down. Ours then goes into the dishwasher and come out sparkling clean. Can’t put cast-iron in the dishwasher. We use cast-iron for some foods - for baking cornbread mostly.