They're probably not moving effective relievers who are under team control through the 2024 season.
They won’t give him away but a rebuilding team might be willing to move a middle reliever who they use even when behind. Yeah, you’d have to give up something of value. Point is quite a few guys like this are out there.
You can't keep complaining about thrown together bull pens. At some point you're going to have to give up something to get some young arms like KC's.