Robert didn't hold the kingdom together, Jon Arryn did. The only good Robert did was stay alive to keep every other family or person from making their power move for the throne. He had the loyalty of the Starks and Arryns and Tullys by proxy, was bound to the Lannisters by marriage, and kept his brothers' ambitions in line. Arryn appeased the Martells and the Tyrells weren't going to rise up on their own, especially Renly gave them a means to grab power. The only real challenge was dealing with Balon Greyjoy's ill-conceived rebellion.
Robert was fit to win the throne but not rule it, he was fortunate to have Jon Arryn to do the latter. I forget if it was in the books or I just read it elsewhere, but Robert should have been born a Dothraki.