Sorry, I don't agree. That's part of the philosophy most airlines follow that the F/O is just a Capt in training. You send the pilots (both CA's and F/O's) to school and you teach them.
At TWA (and I'm sure most of the others) if it was the F/O's leg (so he would be doing the PA's) and it got bumpy HE would make the PA and turn on the seat belt sign. Of course usually you might comment: "Hey, I'm going to seat them". CRM and all that.
As far as F/O's not like making PA's; that is part of preparing to upgrade some day! One less thing to get used to doing when you go to Captain school. Yes, if your company has a culture where the left seater does most of the PA's then yes, it would not be routine for the F/O. Again at my old airline it was normal for the F/O to make the PA's on his leg and we knew how to do it right. When you went to CA school it was a non-event.
Your logic is understandable but you fail to realize two things:
1) AA F/Os currently have at least a 20 year upgrade from newhire to CA so nobody is in any rush to "practice CA stuff." That said, when an F/O is within a couple years of upgrading, most CAs will actively encourage them to start practicing stuff such as PAs and other CA duties
2) AA has a culture very heavy in ancestral worship. To get the flight dept to change a procedure that has been done the same way for fifty years is next to impossible. The PA is just one of those things - AA deems it more important for the pax to hear from the CA, always has. We F/Os don't take it personally, and we just don't get why making a PA is sooooo important in practicing to make CA. Last time I made one it was almost anticlimatic. Big deal. I'd rather not make them, one less thing to have to worry about. We get plenty of practice playing CA on our legs, anyway.