I doubt Saudi Arabia, the UAE, and Jordan can keep the peace alone. Iraq is somewhat our ally anyway. I think the USA will have to have a large enough presence so our soldiers are not targets.
A return to Iraq, more than just a contingency, is about settling the tensions between Israel and Iran. Iran cannot continue its madman strategy of backing terrorists with religious hatred as a priority. It would be to end any conflict between Iran and Israel before it gets started.
The USA presence would have a different tone than last time. I think the urban warfare in Iraq is over. This would be about stability and working with allies in the region to prevent Iranian stupidity from engaging NATO.
My most sincerest wishes are for those wounded to recover quickly and return to their families. They are very brave people to be engaged remotely for the purpose of peace.