Do you think the First Great Council was a sham? It seems likely that Jaehaerys favored Viserys and knew that most lords would also so I think he wanted to add legitimacy to the claim by putting it to a council, as well as satisfy his own conciliatory urges. If push came to shove I’m sure Jaehaerys, a universally revered king, could have forced the issue if he had to and there would not have been serious push-back outside of the Velaryons and maybe Alyssane.