I wonder if they're something better than minting and melting? If you melt a dime you get a little clump of copper and nickel that certainly isn't worth 10 cents (maybe half?). It's no longer money. And melting just intuitively sounds devaluing. But with Cashu to Lightning it's still Bitcoin, still money, still transacts on tap.

"Withdraw cash" and "deposit cash" seems much cleaner to me. The real bank is the Lightning Network, Cashu mints are just the tellers.

In fact if I could remake the whole metaphor that's how I'd do it. Instead of mints there are tellers, with the footnote that cash you withdraw from a certain teller you can only deposit back to that same teller. Call it the picky teller metaphor.