I am not aware of any studies. But I don't think the priority tags mean much for US airlines, and not so much for European airlines, either. With Asian airlines you will get faster delivery of luggage to the belt but that's about it.

I have had misplaced or broken luggage with any number of airlines over the years and the priority tags don't mean much. As an SQ PPS member I had a hard case smashed flat in KUL and delivered to me in a box. But it took them 5 hours to find an empty cardboard box to put everything in so they delivered that to my hotel maybe 6 hours after I checked in. They hadn't said anything to me at the airport other than to fill out a form. At least they followed up with a phone call that evening.

And as a GS with UA I once had 2 checked bags not make it onto my flight to CTU (China) and was in transit in SFO for 5 full days. They were supposed to redirect it to Shanghai but that did not happen and the luggage arrived in Chengdu to sit for another 2 days before some called and told me I would have to go to SHA that night to pick it up. On another trip when I was spending one work day in Montreal on a long multi-city trip when no one on my flight got their luggage. I did get some kind of special treatment I guess because UA kept it when it arrived and escorted me backwards through Customs to claim it, clear Customs, and then check it to board my departing flight that evening when I went back to the airport.

I have had these these issues over the years up with AA, QF, DL, HX, LH, SQ, CX, UA and CA. I can't say any one airline handled the situation especially well. None seem to make it a priority and sometimes it was a total mess. DL had my bag once for 11 days before suddenly discovering it. But I did get it back.

Is it worth it to fly premium? Personally I vote yes but not for any special luggage handling. Better seats, less waiting in line makes for less wear and tear as I get older. Fly safe!