Historically, there was no real battle for Rome either, for much the same reasons.
However, this game makes Rome more important by assigning 12 capacity to it, which means a 37% reduction in German capacity when the Allies take it. I'm into June 1944 in another campaign game using v1.03 as Germans vs favored Allied AI and still holding a line at Rome. Trying to maintain full capacity for as long as possible is a motivator for me as a player, to be balanced against losses I'm taking now that Allies have clear weather and are gaining ground. Perhaps Rome should not have more importance in the game than it did historically, for both sides. Maybe consider adding Florence as another German supply source and split the Rome capacity between them? But if Rome remains as important as it is, then players and the AI for both sides should fight for it accordingly.
I do have a couple of comments about my current game. I let Foggia airbase go too soon, which opened up central Italy for invasion. So Allies landed at Civitavecchia north of Rome around October 1943 and I had to deal with that for several months. One of the units was GBR 4th Arm, which gets withdrawn in January 1944. It was holding the port when it got withdrawn, allowing me to move in and cut off the US 3rd Inf which had advanced into the hills toward Rome. So that's an Allied AI weakness where it should have reinforced the invasion with another unit or two, or at least recognize the imminent withdrawal of a unit and fall back to defend the beachhead. My other thought is whether the Allies should even be allowed to invade that far north in 1943 even if they have captured Foggia but not yet captured Naples. It's a risky maneuver.