Because it makes the nobility stronger
The reason that they're so in favor of this, even universally so, is that this is (seemingly) great for the nobility (i.e. those very same electors). What they are essentially doing is trading a system where the queen or king of the realm has total control over the power of succession for one where the nobility controls it. This dramatically increases their own powers: a king or queen cannot antagonize the nobility nearly as much without fear of losing the succession of their children or other favored successor, which gives the nobility a more flexible lever than the threat of rebellion to argue for their own interests. It also implicitly situates the ruler as ruling by the consent of their nobles, making it potentially easier for the nobles to remove a less favored ruler if the occasion arises. In other words: a weaker ruler means stronger nobles.
We can see this in what they say that the meeting:
Bran has no interest in ruling and he can't father children. Good.
Sons of kings can be cruel and stupid, as you well know. His will
never torment us
That he has no interest in ruling is presented as a positive because the nobility does not want him to have the traditional measure of control. If they were afraid that the lack of a determined monarch would bring chaos, they wouldn't see this as a good thing.
A system where the nobility is more powerful is also a system where kingdoms with pretensions to independence, such as the Iron Islands or Dorne, can more easily pursue it, and possibly even with an eventual legal argument on their side.
And what's more, Bran has no objection to this, whereas any other ruler, who would be able to have children or even be more invested in temporal rules and traditions than Bran, would naturally object to their heirs not being able to inherit.
If any of them don't yet understand the scope of Bran's powers and still see him as weak (mentally or otherwise), they also may well see him as likely to allow them to take more power for themselves.
Because he'll be a good ruler
If any of them do care somewhat about the quality of the person who's in charge of the realm, as even a self-interested noble should, since their people's success is to some extent their own, and they actually understand what Bran is capable of, then they should support him.
With his unique powers, he brings a lot of talents to the table. Militarily, he can foresee troop movements with a precision accessible to no other ruler, through greensight and warging. In terms of arbitration, he will be fair and honest, because of his personality and because of his ability to know what lies behind a dispute. In terms of his ability to keep the realm together, no one will dare speak of open rebellion once his abilities become known, for fear that he'll be aware of it. With his knowledge of what's happening throughout the realm, he will be an unparalleled administrator. He also seems quite intelligent, if aloof, and not unstable like, I don't know, the last three rulers?