This is a design I photoshopped up. $289 Smittybilt SRC roof rack, 60$ cot tent, 30$ ply wood hinge fold out base for tent to mount on and 10$ in mounting hardware, tie downs, straps.
Less than $400 to have a functional rooftop mounting situation for my once a month camping trip with the guys.
Away from the critters, and it all is kept in the backseat (aside from the rack) which is left on the whole time. When I get to my campsite I simply attach the play wood base on the rack, release the tent and strap it all down secure.
Bear with me for a minute, and don't skim the next two paragraphs.
There are a couple of factors that you need to consider, the first of which is the size and weight of your support platform. Cots similar to the one you depicted are approximately 90" long and 30"-36" wide; assuming that you have a single-fold platform built from 3/4" plywood (inference, based on what you've said so far) you'll need to make room inside your TJ for a 45" by 36"-ish object that weighs about 50 pounds...and that weight assumes that you won't reinforce it in any way, which I wouldn't advise. Plywood is incredibly weak across its surface, so it's more realistic to think about what kind of fold-up structure you can build that will be strong enough to support the weight of you and your tent-cot ...and unless you start getting creative with aluminum and/or some structural panel materials, you're probably going to
easily hit the 50-lb. mark when you achieve that goal, and it's going to cost more than $30. You'll also have to take that platform in and out of your TJ, from the top of all the rest of your gear, and install it on the rack
before you can set up the tent.
The second factor you need to consider is weight. If you somehow build a 50-lb. support platform you still have to put a tent-cot on it that weighs around 30 pounds; the Kamp-Rite is 32, and other options are even heavier. That puts you in the 80-lb. range of weight before you add a sleeping bag, pillow, any other gear you might want inside the tent, and yourself. That leaves you with only 220 pounds of weight capacity on the rack, because Smittybilt rates the SRC TJ rack at - and this is a direct quote - "300 lbs. of evenly distributed cargo." Most racks in that category are rated at a similar capacity.
The point of this is that it's not quite as simple as you made it out to be, nor will it realistically be as cheap, and it although your setup plan sounds simple, it isn't. Imagine having to do what you're talking about doing in the middle of a rainstorm, late at night, in the cold; things get immensely different when factors like that are involved.
For those saying to just tent on the ground, that’s not an option, my only other option is to convert the inside of my TJ to sleep in. As it’s my daily driver and it’s too much hassle to take out the backseat once a month, I need a rtt. Worst case if my idea doesn’t work I figure I can always keep my tent for other camping. The rack is useful and I can reuse the plywood and straps for other uses. I don’t see anything to lose.
Camping on the ground
is an option; you just need to figure out how to do it. Personally, I think it makes more sense to modify a tent-cot to be used on soft ground; at least then you're not having to take a platform out, bolt it to the rack, and then strap a cot down on top of it in less-than-ideal conditions. Also, I can't see why taking the backseat out is too much hassle; it literally takes a couple of minutes, and that's if you're taking your time. It's less effort than what you're talking about doing with the platform.
Think of it this way: you're building something that nobody builds...so there may be a reason for that. I love the ingenuity of the idea, but don't make the mistake of assuming success while shorting a proven method. If you really want to throw a rooftop on your rig, fine: do so...but buy a good rack, and buy a good tent. If you absolutely insist on going the cot-and-platform route, take a few pointers from the excellent photos that Mr. Bills just posted and try to replicate those Landcruiser setups on your TJ.