My initial strategy was to drop it on the hex right below Rome, thereby putting out of supplies all German units. However, the AI sees the problem and initiates a counterattack on its turn with all available units until the para is destroyed. Hence, I got few strategic benefits: a destroyed elite unit vs. a few German units out of position (and out of supply for 1 turn).
However, I tried an even more devious plan

At any rate, the followup AI actions also lack sense. It wastes its air attack on some random units of mine. Then tries to counterattack with the panzergrenadier divisions in the area, but accross the river! So no armor shift, and a river downshift. My para successfully resisted 2 panzergrenadier attack, AND the Fallschirmjager attack in Rome (which didn't want to leave the city, likely due to the objective on it). If it hadn't destroyed the brigdes first, it would have been quite easy to send a panzergrenadier on the other side of Rome's river to destroy or at least soften up the para.
Start of second turn On my turn, I used the air supply action, and pulled it back behind the second river. Then, on the AI's turn, it continued into nonsense by not sending any units at all to destroy the two step para. It seems that it froze all units arround Rome? I remember in UOC 1, one of the AI trigger on objectives forced any unit on it to stay there, no matter the situation. However, you could also force any units in the surrounding hexes to stay there as well, if that option was checked. I'm betting that's what may have happened: all units around Rome had to stay there, and no other units could reach the para. Therefore, the AI could do nothing about that two step unit on its last supply route.
Start of third turn Overall, the AI's use of "destroy bridge" leaves much to be desired. Here are some issues that I've seen, alone or combined
- A lone unit advancing by itself triggers massive bridge demolition, despite the AI having enough units in the area to stop it/destroy it
- The AI blows up the bridge before retreating its units
- The AI blows up bridges without regard for future supply situations
- The AI blows up the bridge while the HQ is on the wrong side of the river
- The AI becomes trigger happy after you've built a few pontoons (nice exploit to distact it from blowing up the bridges that matter)
- The AI blocks its attacks/counterattacks by blowing up bridges
