He asked him because he was off his rocker. However, it seemed to me the seed singing was a big deal. Why wouldn't he have participated. In the Rhuidean flashbacks the Aiel speak of having Aes Sedai travel with them and of Aes Sedai healing arthritis. Remember, their title was "servant of all".
Also, the Song the Aiel sing outside the gate IMO is just a standard Seed Song. The Aiel sing it to remind him of how the world was before the breaking when the power was used to creating rather than destroying and of the peace that the Aiel stood for and the Aes Sedai helped to foster.

Additionally. I can't help but notice how often on forums people throw in whole new ideas (like the thought that there are many songs) on a single line that does NOT say that just possibly makes more sense if that were the case. One could equally say the Aiel song they sang to the Aes Sedai that he gates(Mondaran was it?) to remind him of who he was, was a song that: cured insanity, nullified the one power(remember people escaped the city--that was the Aiel's true goal there), put him in a trance, OR was the famous Seed Song and it reminded him of a time of peace before the DO came out. People always try to add things to the story because it fit's their view. I know, I catch myself doing it a lot. It is an especially slippery slope when already out on a limb trying to predict future plot development based on fragments here or there.