You could both get upgraded and get not-together seats. If you end up with one window and one aisle, it's usually very easy to get one of the other folks to move..because it's to a like seat.
This can indeed be "very easy", and I've had a couple of very pleasant experiences, but it can also be a non-starter. People have very different ideas about what constitutes a "like seat": less legroom on LH side of MD-80s, bulkhead/not bulkhead, too near galley/toilets/coach, FEBO-disadvantage...) And some are just extremely attached to the seats they've made an effort to secure. Something I can understand to a point, but sometimes it smacks more of bloody-mindedness. Either way, sitting in 6A with your other half in 3B isn't a great start to a weekend away together.
Definitely a case of YMMV, but my wife and I try to avoid late upgrades on longer flights. We managed to give one back at the airport last week (YVR-DFW), which doubtless made two individual travellers happier than they would otherwise have been ('twas a 757..

).
No idea why AA can't simply add an option to specify "adjoining seats or no upgrade" on the request screen.
Lone passengers could also help, of course, by remembering that there are unlikely to be many empty seats in the front cabin by the time the plane takes off. Bagging 5E rather than 4E, because 4F is 'taken' when you select your seat from the seat map, is unlikely to bring any reward. It's understandable, but ultimately misguided, selfishness that just makes it harder for couples/friends travelling together: the chances are that 5F, too, will be occupied.
There are plenty of cooperative people, of course. On one memorable occasion (it was only our second or third AA upgrade, an evening DFW-SEA flight) a guy swapped seats even though it wasn't a "good deal" for him: he got a window seat on the left and gave up his preferred aisle seat on the right. It was nice to see him 'rewarded': he found plenty to talk about with his new neighbour, they clearly enjoyed each other's company for dinner and drinks and exchanged cards on landing.