She won't do this because she is not a complete and total moron. See, the VAST MAJORITY of enemies whom damane face are NOT channelers and NOT susceptible to shields. Logic would therefore suggest that since the Seanchan sul'dam and damane are USED to facing people whom they cannot shield, they have devised other methods of dealing with them. Lightning bolts. Fireballs. Crap like that. Your suggestion would result in 2000 dead Aes Sedai right quick. The ability to link did not save them from the Shaido Wise Ones or Asha'man at Dumai's Wells after all.

When you link, you basically do nothing other than create a super-strong channeler. You trade a bunch of little guns for one big gun. The other people in the link are merely ambulatory magazines or batteries. Given their inability to fight without their lives being threatened, and their certain knowledge that the Seanchan would prefer to take them alive, the circles jumping into Seanchan territory will not have any first strike capability and very little practice using the Power as a weapon, whereas the Seanchan have institutionalized procedures and practices. Alivia's skill with weapon weaves might not be shared by all the damane, but you can bet the sul'dam have it all down. They view the White Tower as their greatest adversary and believe all other opposition they have faced thus far is connected to the Tower. Do you REALLY think they don't have contingency plans for an army of channelers appearing in their midst? After initial attempts to shield the sisters fail, they will simply start trying to kill them.

The Seanchan collar channelers primarily because they need them to fight other channelers - their top priority is control of all channelers, NOT having the Power. If they cannot leash the channelers, they will destroy them, rather than leave mareth'damane free.