Hi!
We bought one for our kids a few years ago for all the reasons you mentioned. We bought a round one. I actually haven't seen a rectangular one in years, but I'm sure they are still out there. We did put ours in at ground level which was a big pain but I do think is much safer. The only incident we had was before we dug the pit, and it was merely someone who was walking (not even jumping!) that fell off and landed in a nearby bush. She was a little scraped up. Our neighbors, who do not have theirs' ground level and no net, had a girl fall off and ended up with a bad arm break. As for rules, we always insist on parental permission for friends before the initial time they jump. When I was growing up, some of our neighbors' parents insisted on written permission. I would definitely make sure it's ok with parents either way, in case of an accident. We do allow more than one kid to be on the tramp, but only one can jump at a time. Double jumping can cause one of the jumpers to fly very high up if they land simultaneously, and they may not land where they should. But if they have some games such as crack the egg, then several children sitting on the tramp seems fine. On the plus side, it does give them another option for exercise- and yes, Mom as well! And the novelty definitely wears off, probably more with how long you own it than any particular age. My son doesn't use it at all any more, but both my girls get on it occasionally. Oh, and another thing you have to think about with rules is whether you want them to do flips, which is where many of the neck injuries happen. And, of course, no one can jump when Mom an Dad are not home!
Good luck with your decision, and have fun with it if you get it!