I think the only problem with this is that the Ajah gained influence when they brought stronger Novices to the Tower, and by extension, there are indications that a Sister who found a stronger Novice would gain some sort of influence as well (i.e. scene where Moiraine tells Siuan that she has found a much stronger channeler than Nynaeve - she doesn't mention this as an aside, but as a politically significant addendum that could shield Moiraine from trouble).

And we already know that age and rank resulted in deference, so you couldn't necessarily browbeat any Sister weaker in the Power.

And ultimately, every Aes Sedai was concerned with finding, and bringing the strongest and most intelligent channelers to the Tower. To add to this, Elaida pushed Moiraine and Siuan extremely hard after she was Raised because she explicitly wanted them to pass - she didn't necessarily seem to think that they would support her politically, and seemed to think they needed to pass for the good of the Tower.

All in all, I think the culture of the Tower was one which favored finding and training the strongest channelers possible, and I don't think the vast majority of Sisters were so petty that they would purposefully avoid bringing promising candidates to the Tower even if that candidate had a higher potential than them.