I don't feel this this right and the math must be a little off... A bumper pull trailer puts the pin weight BEHIND and only SOMETIMES level with the rear axel even with the weight distribution gear. A gooseneck/5th wheel puts the pin weight usually directly over if not slightly forward and ABOVE the rear axel... You can tow weigh more with an over/in the bed hitch then a bumper pull. 5th wheel trailers are designed to keep pin weight within usual ranges for most truck and have come a long way. You still have to be thoughtful when loading and storing items but in general they handle way, way (yes added the second one lol) then bumper pulls even with a properly set up weight distribution system that from my experience 90% of people don't set up right to begin with.
My 1999 f250 has the camper package (rear overloads, front/rear sway bar, 4way/rv plugs) and has a 10k rated hitch meaning if I use a weight distribution, don't overload tongue weight I can haul 10klbs max... my truck-7640lb on sticker and usually 7900 with me, fuel and gear bringing me to 17900lb which is also under the 21k limit for the truck in total. +/- 500 for gear but I travel light with trailer gear when camping.
If I go 5th wheel or gooseneck legally (this varies by states and locals) but federally i'll be under 26,001 so I can tow 12,500lb with the 5th wheel/gooseneck brining me to 20,400lb +/- 500lb for camping gear, I keep the trailer light when camping. in total still keeping me under the 21k max gross combined. Im only 90% sure my f250 shortbed 4x4 auto is rated at 21k but It could be 22k etc.
You truck will handle a 5th wheel A LOT better then any weight distributed bumper set up and handle more weight to boot. To keep state patrols, dot and other off by back I learned just subtract 1500lb from your gross total combined and pick a trailer in that just in case you need to pack heavy.