My belief is that Bryce isn't a royalist, but rather that he tried to
take the throne once Maric died. He failed, as Loghain, allied with
Eamon and many others, would have a far greater claim but still Bryce
did indeed try I think.It's a good postulation, but incorrect based on what we got in the game. He never tried to claim the throne, and they make a point of bringing that up in game that he had strong support and could have made seriously legit run at being crowned King instead of Calian five years ago, but passed it up.
That's just the Black and White version. He either:
a) Was truly a believer in one of his last lines, 'Couslands always do their duty', so trying to 'jump' succession was a move he would never contemplate. Instead serving dutifully and faithfully to his nations bloodline - which Fereldens, especially veteran families of the rebellion seem to put a lot of stock into. Normally with the Shade of Grey they pump with Dragon Age I'd be inclined to call BS on this, but they really do paint Highever as a sort of Arthurian Legend and many of it's bloodline as 'true' heroes...since they know they are going to smash it down, put it to the torch, and walk away from it half an hour later.

He seriously considered making a run at the throne but never actually did so because of your points. He might have had a strong backing, and a good enough pedigree to make a run at the crown, but he would have had to risk fighting against the Arl's of Redcliffe and Amaranthine, some of the Bannorn, the only other Teryn in the land... it might not have been such a 'lock' so he gracefully bowed out after realizing it would lead to Civil War, or had a high chance of failure.