Quoting to better break down my reply.
But in Atsuyo it was not just the suicide squad that went straight for Kanki. The Ousen army had big problems because of the hate for Kanki too.
Exactly, which is why I say, Zhao currently hates Qin as a whole. But the thing I wanted to point out is that Zhao used soldiers that were personally affected by Kanki's massacre to employ this tactic. And I think that the fact that the Zhao soldiers could see Kanki's flag while the siege was occurring simply fueled that hatred even more so they could throw themselves out.
Remember how Denrimi's ladder strategy didn't really make a progress thanks to the Atsuyo soldiers suicide dives? The entire reason why the Ousen army has three times more losses than calculated is because the soldiers hated Kanki. The only difference between the guys on the wall and those going for Kanki is that the former were just used as fodder to slow Denrimi's attack down while the ladder were the elites who had a chance to actually kill Kanki. But in terms of they felt there's nothing that indicates that there was any difference between the two.
You are right, the suicidal soldiers and the elite forces had nothing that separated them in terms of their hatred for Kanki. Both forces were willing to die to get the job done, and I think that went double because they could see Kanki outside.
So jumping to the current predicament:
The soldiers stationed at Sekirei could turn to be a dangerous force and would become unpredictable (like commit suicide) if they saw Kanki's army ready to siege them. The thoughts of what could happen to them if they lost could make them desperate.
On the other hand, another army would still incur Zhao's wrath, but they might not try any desperate moves or tactics.