Simply put, because if he had backed Richie he wouldn't have any Family to be the Boss of. Everyone else regarded Richie as a punk, pretty much, because while he was a made guy and did his time in prison he had no respect for what had changed and kept trying to ride Jackie's legacy as the reason why he should be given everything on a silver plate.

The fact he couldn't get any support just sealed the deal. Junior made the smart, and correct, move: Tony had respect, people liked him for the most part. He could keep things running. If he had backed Richie, not only would there have been a war but there wouldn't have been anything left after the smoke cleared.