Fedex and UPS ship millions of packages efficiently- would it make sense for an airline to outsource Baggage Handling to one of these guys?

Interesting thought!

Personal perspective: In over 25 years of flying, I've only had two problems - and once was then the tag didn't get stuck on properly so the bag was left behind for four days...(It finally arrived late on Christmas Eve - intact, presents and all). The other time, it was stuff for work which didn't make a quick connection in Paris (it arrived at the client a couple of hours later). Perhaps Too Much Information...

BTW, have you noticed that some airlines reward early check in with a FIFO rather than LIFO baggage delivery?

In the spirit of Change is Good, I've extended your concept a step further and assumed that it's not airport handlers you want to replace, but the whole system....

No doubt one would have to convince vested parties that the logistics are sound and that this is a good change - including:
- customs
- immigration
- (homeland) security
- unions

On the plus side, you could create another whole set of work/careers which could be more ecologically sound:
- baggage check-ins / delivery service ahead of time / baggage security (eg someone else can't walk off with your bag if you are behind them in the queue)
- luggage only "flights"
- real double decker passenger services / more space... (need to figure out how to fill up every seat on every flight)

As an added BONUS they could put the planes back near the exit (so you didn't have to walk a kilomile to use of the time so that the luggage would be on the carousel within 15 minutes of clearing customs).