As for the purpose of capturing one of the Twelve Demon Moons, he would probably give it careful thought.
He would also have to consider whether the Demon Slayer Corps might use one of the Twelve Demon Moons to set a trap.
In fact, Tetsu no Sosuke had already thought of plenty of possibilities.
For instance, they could capture a demon from the Twelve Demon Moons, lock him in a large iron cage, and cover it with black cloth... Then, when Kibutsuji Muzan came to rescue him, they could pull off the cloth and let the sunlight kill him.
Of course, that was the simplest plan, and it was full of holes. Even if Kibutsuji Muzan came to the rescue, he would come at night, not during the day.
Covering the cage with black cloth was hardly worth considering, either.
But if they followed that line of thought, a little time to prepare might be enough. Even if they could not kill Kibutsuji Muzan outright, they could at least send him fleeing in disarray.
Yet Tetsu no Sosuke thought something else was far more likely: Kibutsuji Muzan would not come at all!
The man was as skittish as a startled bird now. Would he really come here for this?
Tetsu no Sosuke could not be sure... But whether Kibutsuji Muzan came or not, the Demon Slayer Corps stood to gain.
If he came, they would spring the trap and subdue him.
If he did not, they would have captured one of the Twelve Demon Moons. That might yield more intelligence and allow for deeper research... Either way, it would benefit them.
In short, capturing one would give the Demon Slayer Corps some control over the situation.
Whether Kibutsuji Muzan was willing to be put on the back foot was up