We don’t have to bomb them to extinction. We just need to bomb them so that they can’t threaten the Red Sea with cruise missiles or drones.
This is a group with ships, helicopters, cruise missiles, anti-air, and drones. They’re “large” enough to have legitimate military targets for us to disrupt. Every cruise missile we blow up of theirs is one fewer missile for them to launch into the Red Sea.
EDIT: In particular, all we gotta do is sit there, watch our RADAR. Whenever they launch a cruise missile at the Red Sea, we launch an attack back and kill those people. Eventually they’ll run out of missile-launchers (or people brave enough to push the launch missile button). If that’s a “never”, then I guess we keep patrolling the Red Sea from here on out, but it seems like a rather straightforward, low-risk mission to me. The main risks are the possibility that someone on board of our Destroyers / Cruisers gets complacent and lets a cruise missile through to actually take a hit. But given our anti-air capabilities and RADAR to detect enemy missiles, it seems unlikely that this would happen.