I think they are fairly long to give the option of fitting to lots of cars, the can be adjusted to fit on a hatch, saloon on the boot etc.
They would probably be moved out more at an angle when on the car so it wouldn't be so far out, though probably no more far back than towbar carrier - though not as secure.
Personally I don't like strap on carriers, they just don't look reliable enough to me, but they are a relatively cheap option.
Yup, might work
When I just had a lighting board for such use and no towbar, I just had the socket loose in the rear of the car (stashed in a cubby hole at the side of the boot. The rear hatch would shut ok over the cable.
It was cheap (generic socket on a flying lead, with a beeper) and wiring was easy enough (once I'd identified the relevant wires) I also used a bit of scrap cable to make a couple of connections to to light on the other side.
however, with more modern cars you need to take a bit more care (and expense - though it can be easier as you might not need to do any wiring)). If they have a multiplexed wiring system, then I think you need a special bit that plugs into the wiring system. ditto care is needed with systems that have bulb failure warning.
Websites that sell towbars etc normally have details of what specific cars need.
All car cycle carriers are a compromise - the main compromise with strap on carriers is it's relatively cheap, and it's a faff to fit. I would go for roof mounted or towbar mounted - but this is more expense (though if you have roofbars, roof mounted ones are ok)
To be fair, most rear fitting carriers will require a lighting board, and socket etc.