And Stannis takes the city. What then? If Tommen gets to grandpa in the West, the kingdom is going to be split apart- you can’t crack Casterly Rock, Mace has no love for Stannis (with supporting the entire upsurption and kinslaying), and Robb being King in the North. Could Stannis get support ( even with having no heir beyond a scarred little girl) or does the war get in a stand off?

If Stannis takes the city, first thing that happens is that the half of the Stormlands that’s been holding back declares for Stannis, which starts to change the military math considerably.

And that changes the political math. If all that Tommen is a king in exile in Casterly Rock acknowledged by no one else than the +10K men that Tywin has left, he’s less attractive to anyone outside the Westerlands, while Stannis’ stock will grow from victory. 

Moreover, time is not on the side of the Tyrell-Lannister alliance. Unlike in OTL, they can’t focus their whole army at wiping out the Starks, because Stannis will be a major threat who has to be guarded against. Which is also going to reduce the likelihood of the Red Wedding happening. Moreover, in a few months, Balon’s going to be dead, the North’s going to have a chance to recover, and Euron’s going to attack the Reach – and that’s going to change the appetite of Reachermen for adventurism considerably.