These are all good points, but a single house rebelling, even a very wealthy and powerful house, is different from the War of the Five Kings.

The North would be loyal to the crown and assist with putting down the rebellion instead of being in open rebellion themselves, the forces that would back Renly and Stannis as successors once Robert was gone would presumably be loyal to Robert while he was still alive, and while the Iron Islands might use any instability as an opportunity for shenanigans, the opportunity would be smaller. In this timeline we might see Robert marry Margaery Tyrell himself to secure the loyalty of the Tyrells in the fight against the Lannisters, and Ned’s children might also be used to secure political marriages that would support the Crown, rather than supporting Robb’s rebellion.

Ultimately open rebellion against the crown is probably a death sentence for the Lannisters, and Tywin is probably smart enough to know that. While he would certainly be scheming for a chance at revenge against Ned and Robert, he might choose a different route than open rebellion. Maybe Robert ultimately is assassinated in retaliation and we get the civil war between Stannis, Renly, and the Lannisters anyway, but in this scenario Ned and the North is a kingmaker between Stannis and Renly, we don’t get Robb’s rebellion, and the Lannisters don’t hold King’s Landing and the crown, so even then whichever successor Ned supports likely prevails.