"Unibody" trucks have been done; Ford had one in the '60s and of course there are littler ones like Ridgeline, VW Caddy, utes, and so on.
The '60s Ford was still body-on-frame but I've read there were complaints that the doors were hard to open/shut or wouldn't open/shut if the truck were heavily loaded, especially a few years on with rust. Oops. Helps to isolate the cab from those stresses. Yes, I know this only applies to the 1% of pickups that are called upon to haul more than groceries.
But I think the main thing is that a "uni-cab" reduces the versatility of the layout as seen when boxes are removed and replaced with dump boxes, flatbeds, hi-cubes, etc.
P.S. The truck should still have ALL it's structural integrity without the box and without adding braces and such when sans box.
P.P.S. And the thing shouldn't fold in half 10 years down the road when you put a load on it and the tin is compromised by RUST (since the mfgs design their junk to rust out
on purpose at about 10 years in the Rust Belt).