There are some fifth-wheel hitches which are not removeable, but they are usually used on larger commercial trucks (directly on the truck's frame rails, or on a flatbed deck), not in the box of a pickup truck.
In addition to the visible rails, hidden brackets under the box floor are also left in place... which is as intended and presumably not a problem. The hitch is often in multiple pieces, so that it can be lifted out more easily - the whole thing is heavy!
The rail-mounting design has one nice feature: the same base rails are used by multiple manufacturers, so you would have some choice of hitches without changing the permanently installed parts.
There are also systems which are even less intrusive when removed than those using cross-rails:
Reese Elite series (only; other removeable Reese series use rails) has mounting pads or "pucks" - Ford offers this as a factory option
B&W Companion OEM system works with the same pucks
B&W Companion works with their Turnover Ball under-floor structure
Most of these non-rail systems are pretty big for an Escape 5.0; they would work fine, but might be heavier or bulkier than needed.
I have noticed that some people in RV parks with a fifth-wheel trailer for an extended period (such as over a winter) remove the hitch head from the truck leave it attached to the trailer, hanging in the air. I suppose it doesn't get misplaced that way, is out of the way, and stays clean and dry... and of course it's not in the way in the truck box.