I'd rather have the Asha'man running free to fight as they have been trained, than contributing their strength to an Aes Sedai shackled by the Three Oaths and an ingrained reluctance to do anything useful with the Power.

Look at what happened at the Cleansing, the one time we have seen Asha'man and Aes Sedai cooperating like that - the Aes Sedai screwed the pooch hard. The best showing was by the circle led by an Asha'man, which thwarted and drove off Demandred, and Alivia who faced off with Cyndane. Verin got one of her people killed by trying to capture Graendal instead of kill her, which sacrificed the little initiative she had (no way a Forsaken lets a linked circle strike her first unless they caught her by surprise). Big surprise, the Brown thinks of the potential for gaining knowledge, rather than DOING HER JOB which is to protect the single most important feat of channeling since LTT sealed the Bore. We also see Daigian, whom Cadsuane stupidly puts in command of a circle because she respects her abstract intelligence, get her warder killed (and fittingly this causes her to get killed later in Semirhage's escape) because she also sacrificed initiative by not drawing full on the Power. If Eben had not been in a link, he would have been able to strike at Aran'gar with the Power, rather than physically, and stood a better chance of A. surviving and B. hurting her. Daigian was not even drawing on more of his strength than was absolutely necessary to maintain the link. You can bet that Eben (or any Asha'man) would have been holding all of saidin he could if he was out patrolling on the off-chance of spotting a Forsaken! Finally, we have Merise who passed control of the circle to a visibly unstable, and as it turned out, Darkfriend, rather than shoulder the distasteful burden of channeling the flows of saidin, which would have been the greater part of their circle. She abandoned her responsibility because it was uncomfortable. Of course it turned out for the better, as Elza knew (why else do you think she was ready to beg for cotnrol - she knew she would be better able to defend Rand without the Three Oaths impeding her), but her for of loyalty to Rand could as easily have mandated she take him prisoner and carry him off to Shayol Ghul to turned to the Great Lord by a circle of 13 and Myrdraal, be made Chosen and granted immortality! Lucky for the world, Elza is an Aes Sedai and thus an idiot, or Merise could have lost the entire fight by giving up the job Cadsuane entrusted her with. She trusted Merise most among all her followers, according to Cadsuane herself, and if anyone had any doubts about that, her giving Callandor to Merise would have clearly established that. But Merise chickens out.

All in all, placing Asha'man under the command of Aes Sedai, or counting on Aes Sedai in a stand-up fight is a BAD idea.