A cheap valve between the hot/cold valves and the bath faucet or showerhead can provide that. Unfortunately, single-handle mixer valves aren't usually designed

A cheap valve between the hot/cold valves and the bath faucet or showerhead can provide that. Unfortunately, single-handle mixer valves aren't usually designed to have their output blocked under pessure like that. So that's when it starts getting expensive and specialized. But with traditional separate hot/cold valves, it works fine.