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As little as possible, it's just about as bad as weight on a roof rack for vehicle dynamics.
I agree, let's call it a necessary evil.
It shouldn't be done without some serious consideration, or when it's the only option. However, there are ways to do so lightly, and compensating with proper suspension, vehicle handling is still bearable.

Well, that can be true for some, but as mentioned previously, it can hardly be a generalization. I realize now I didn't respond on my first post when saying this.
There is stuff you don't want inside your vehicle: fuel is one of them. There's two ways to carry fuel: A fuel can or two if you don't need much, or a fuel tank if you need a lot. Where can you carry fuel cans? Either a swingout or your roof, no other option.
When it comes to aux fuel tanks, the most usual place is where your spare sits under the car. This is the main reason why I install rear bumper and swingout. Get your spare out of the way, mount a fuel tank and be done with it.
Anything else will depend on your needs and vehicle, obviously, and it will be a compromise as with everything. But just because you can use a swingout as a tool doesn't mean you have the wrong platform or idea.

Box with all the gussets and supports weighs ~140kg. Contains 200kg of metallic type recovery gear like chains, Unimog sized shackles, pulleys, jacks, etc. Along with replacement of un-needed generator with fuel tank in front of rear axle (allows running with rear tanks empty) and switch from propane to induction cooktop (removal of 2x30 lb cylinders from behind rear axle), it improved weight distribution from 35/65 to 41/59. Beneficial effects on handling immediately noticeable.
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I generally think carrying boxes of stuff on the roof of high vehicles is silly but people who drive Unimogs and/or live in Alaska get special treatment.
If I lived in Alaska I would probably just have a machine gun in a turret on the roof filled with whatever ammo kills bears and moose.

And 10 minutes ago a family of a mama lynx plus 2 kittens sauntered by 30’ from my deck.I hope you’re kidding. Yes I carry a firearm (a fairly big one) when camping in Alaska especially when hiking in “the middle of nowhere” with grandchildren. But I don’t de compensate when traveling in Canada or any other country when I don’t have one. Even in Southern Africa with lions, hippos, crocs and black mambas (all of which I’ve had “close encounters”).
I previously was carrying all the junk in the box in the rear storage compartment. But the truck is better moving a lot of weight from behind rear axle to in front of front axle.
Actually even in Alaska humans are a lot scarier than the Pleistocene megafauna that remains. On my unarmed daily 2 mile constitutional in my edge of wilderness neighborhood, I see bears and especially moose frequently. You just need to respect their space.