Then it depends on such time as when Robert was proclaimed king in general, but from all indications from GRRM himself Robert only told Ned and Jon Arryn his intention to take the throne before the Trident, not that had been declared King yet, so until such time as such a legal proclamation was made everyone wouldn’t have sworn an official oath of loyalty to him yet, wouldn’t you say? Also wasn’t Richard II recognized as the official heir of his grandfather after his father’ death?

I don’t think that’s what GRRM has indicated.

Indeed, the politics cut absolutely the other way. After the Battle of the Bells, you have all of the rebel houses gathered together for the first time. And you’re already in the process of solidifying ties between them – hence the decision to marry Ned to Catelyn and Jon Arryn to Lysa to secure Hoster Tully’s support. 

Rather, you’d want as public a ceremony as possible with as many participants as possible, because you want everyone confirming their loyalties to Robert ahead of a major battle against the enemy, just in case anyone gets cold feet about going up against a royal army. And this was a real worry: at the Battle of Ludford Bridge in 1459, Richard Duke of York and Richard Neville the Kingmaker had to flee because Henry VI appeared in person on the battlefield for the first time, announced a pardon to anyone who would change sides, and a significant number of Yorkists defected during the night.