Once Robert rebelled, he upset that balance. Suddenly the great houses were not equal, the Baratheons became the royal family by conquest. Fourteen years was not enough time to establish their rule as a precedent. Why should Joffrey (even if he was Robert's son) rule? Why not Stannis or Renly? Why not Robb Stark or Balon Greyjoy? Once the Targaryans are out of the picture it becomes a free-for-all.
Having a Baratheon for King of the Seven Kingdoms is not really the same as Robb Stark or Balon Greyjoy claiming this title, though. Robert's claim to the throne was that he himself was related to House Targaryen - via his grandmother, if memory serves. It wasn't as strong a claim to the Iron Throne as any of the surviving Targaryen relatives, but it was a
claim, which is significantly more then either Jon Arryn or Ned Stark ever had.
This is why Robb Stark and Balon Greyjoy both go for individual kingship titles, North (plus Trident) and Iron Islands, respectively, because those are ones they can lay claim to from family lineage... while Euron Greyjoy wants a match with Daenerys Targaryen because basically anyone who married her would have an automatic claim on the Iron Throne.