Not sure I agree with this, power input shouldn't be what determines using Conqueror's Haki or not, otherwise all he has to do is use his strongest attacks. He should be able to do it with a basic attack just like Luffy uses it in base form.
The issue is not the strength of the attack, the issue seems to be that he just lacks control which is natural, he is only just learning he has it, and only just learning how to control it. Zoro is unable to distinguish between his Armament and Conquerors, it seems he just needs better awareness of it, and then he will be able to control it more. He is gradually getting there by the looks of it.
On top of that, just like we saw in Wano, when Luffy tried to Force non-touch Haki, he couldn't do it, and then when he needed to do it, he did it instinctively. Zoro is trying to force it, it seems perhaps, the best way to control Conqueror's is not by forcing it, at least that might be a key to it.
What may even happen is Zoro may not kill Sommers, he might just injure him critically, and then Imu, Killingham and Sommers escape or return back to the holy Land, I'd imagine since there is a pentagram in Elbaph, that is a route of escape. Not sure a Holy Knight should die so suddenly, and more so someone who has been around for a long time during flashbacks.
We are all assuming that Zoro and Sanji defeating the Knights weakens Imu and then Luffy defeats him. I would also entertain the possibility Luffy defeats Imu, and then the Knights end up leaving and escaping as an alternative to this. Will wait for a better translation since this wasn't very clear - at least, the one I read.
To be fair, Hannibal, I struggled putting my thoughts into words, and I don't think I really disagree with you.
I'll try by using your words to further express my thoughts.
power input shouldn't be what determines using Conqueror's Haki or not-->
I agree. What I'm more saying is like... what makes that tiger attack he used different than the pound cannon. It's not necessarily the power itself, but rather the implicit recognition of a hierarchy of attacks.
I know you believe there is a hierarchy of attacks. So I'm sure that you would agree that Zoro is capable of threat assessment of "I should try harder" for this situation.
I think it's the instinct to know when he needs to exert more strength. So not necessarily just power input, but it will look like that because the "recognition" that he has to use more power will drag the Conq out.
So that would be how I would correct my previous statement. The recognition of an internal hierarchy, or recognition of one's own power and the application of it, is what's pulling the Conq out. And I think that pairs better with Mihawk's rhetoric.
So, just as Sommers was observing, when Zoro needs to do something like cut the vines, he will know he has to put oomph in it, and that mental process will pull the conq out naturally.
When he needs to use Pound, he knows it requires a certain amount of muscle strength, and in doing so, the conq will come out.
Maybe we can sum it to, when Zoro recognizes he needs to exert himself more, the conq will naturally follow. And again, that fits with the phenomenon we're seeing.
And I do think it's a subconscious thought. Not a loud thought, which is why Zoro might be having trouble picking it out.
I'm just putting more thoughts into word:
What is the thought process Zoro goes through to decide if he needs Armament or not for an attack? Within that thought process is the key intention the Conq is following. Like its, it's the recognition of I have to be stronger or exude more strength/attack power/cutting power.
Maybe he has to be thinking at all times that he needs to exude strength, even if the attack he is executing doesn't have the high base power of something like pound cannon.