I believe the F450 still has a boxed frame. Some of the chassis variants of the Super Duty still use C-channel, but according to Ford, that's to allow for easier modifications for contractor and commercial applications. All of Ford's literature has emphasized that their new boxed frame is stronger and more robust than the previous c-channel versions.
The domestic trucks have been boxing their frames since at least 10 years ago, if not earlier (Ford's Super Duty was the main exception until just recently). Toyota still boxes their frames on all of their 4x4's and pickup's (the North America-produced Tacoma and Tundra/Sequoia being the only exceptions). I suspect cost and weight savings are the main reasons behind Toyota's decision with those 2 platforms.
And your point about frame twist with heavy loads illustrates exactly why most pickups (whether they be HD or not)
should have boxed frames. A big commerical truck driving along a mostly flat road is fine with a c-channel. For a Power Wagon or comparable 3/4 ton carrying a camper on a rough 4wd road, the boxed frame makes more sense.
That said, both of Toyota's C-channel pickup's are well made and reliable. I wouldn't refrain from buying one simply because of their frame design. I just wish Toyota would follow the example of all the other truck makers.
No, just no.
F-150's still use boxed frames:
http://thenewswheel.com/2015-ford-f-150-frame-creates-better-performance-toughness-efficiency/
http://news.pickuptrucks.com/2017/11/fords-f-150-frame-extenders-look-sturdy.html
The fully boxed method is not a fad. Pretty much all trucks, from mid-sized to 1 ton's, do use that method with the exception of the 2 North-American pickup's Toyota makes.
It is not the frame's job to flex and allow for better ride; that's the suspension's job. The only vehicle that has a frame which was specifically designed to flex is the Unimog. All other vehicles have frame flex to varying degrees, but that's an inherent compromise that engineers have to deal with.
If a boxed frame is well-made, and the proper payload is observed, the frame will not bend or break. Of course, I've heard of broken frames, but it certainly isn't a common trend with modern frames, whether they be c-channel or boxed.