As far as we know, multiple other factors are considered before strength in those matters (just like strength is only one factor in the choice of Sitters). Aes Sedai are not completely stupid. They would consider experience and skill, and a personality suitable to that of the leader. It's the same for ambassadors, not chosen exclusively because of strength. Verin was able to influence so much the Salidar embassy because she outranked all of them and not being part of the embassy she wasn't placed under the authority of its leader (who wasn't the strongest of the lot, the Hall simply put her in charge), then Bera and Kiruna arrived and outranked all of them again and took control. So clearly the women the Hall had chosen to be Rand's advisors were not the strongest available...

Now if you're saying that Elaida's strength was probably a factor in the fact someone as young as she was was able to retain the position she had grabbed for herself, you're probably right. It would at least have stiffled protest, if the Hall had any reason to protest, and mind you the fact Morgase accepted her as advisor while High Seat probably counted just as much. She may even have asked Elaida to stay as advisor once she got the crown. Elaida was also the protégée of Galina, so no doubt she had strong support from the three Red Sitters.

When it comes to politics/diplomacy, Aes Sedai don't rely solely or evem mostly on strength. Some of the Sitters are just above average. It's more that strength gives you a big advantage even there, but aside from Joline and Teslyn who were atypical as they were sent as advisors to humiliate them, we just have Elaida/Gitara as evidence a strong woman might be preferred for Andor, and it might have more to do with Gitara's strong personality than anything, and we know Elaida grabbed the position for herself without an appointement.