Amman was fine, but I don't think you'd miss a lot if you cut it out. We mostly used it as a base between Petra, Jerash, and the Dead Sea.
We did do a Bedouin tent -- Seven Wonders Bedouin Camp -- and it was a pleasant experience for sure. I was hoping for maybe a little more of a cultural experience there -- and to be fair, we were so exhausted that we went to sleep soon after dinner and may have missed it -- but it was a nice place to stay and certainly more interesting than being in a hotel. It's not roughing it by any means. I'd have loved to have really seen the stars when they turn off the outdoor lights (I think at 10) but we were so tired from trekking through the desert we just didn't make it.