I think everybody is missing the worst thing about Bran.
He's the Three Eyed Raven. So like, super prophet guy of the faith of the Old Gods.
Just to comment as someone who casually reads information up on the show rather than watches it firsthand out of curiousity, my analysis is probably very flawed but i believe it delivers enough emphasis to explain why Bran is the worst candidate and a cop-out.
Religion aside, you can suitably say that the Three eyed Raven isn't really truly even Bran, except that the embodyment of the conciousness of the Three eyed Raven who according broadly to lore just hit the jackpot for a seat on the throne by using Bran as a vessel therefore achieving their own goals, wherein being Bran is just a minor detail. Bran had been becoming increasingly alien and distant through his transition, being virtually all warged out with conciousness dispersed all over the place, a little bit in his direwolf, a little bit in Hodor (not at all used at a later date in his wight state) and having his own conciousness dispersed and put aside by the three eyed raven into a void of a personality for logic rather than wise brooding.
The quote unquote "Three Eyed Raven" served the targaryans at the time of the blackfire rebellion i broadly remember from a lore overview from some other filler novels/information J.R.R Martin published as their own person implying the person jumping had been happening for a while because the Three Eyed Raven we meet on the TV series before 'they' become bran must have been exceptionally old. You can either say Bran was the sympathetic or wise figure to influence nomination for the throne, but since Bran is a Stark it seemed pretty obvious some nepotism took place.
Or it was not thought through by the writers at all, which is the most likely conclusion. Bran is more or less already dead, a heretic wizard stranger posing as Bran is on the throne as you point out in a power-play that'll probably ruin and skewer politics completely (not that the iron-throne being melted into slag-metal really helps either) until it all gets undone by some means. Anybody with common sense or similar magical proficiency would not trust someone with machevellian magical abilities and intent even seemingly only beneficial with outcome to become realm regent, so hopefully G.R.R. Martin will kill him off at some point in the books for a shock twist and everyone else.