I think you're mixing up a couple of things here. 120Hz sets display 24fps material by repeating each frame five times per second.
But this doesn't result in the "live" look that you referred to - that's the result of frame interpolation - i.e. "Cinemotion" or "Smooth Motion" or whatever a particular manufacturer calls it. In effect, the set is creating new frames by "guessing" what should be in between the existing frames. This creates motion that is "smoother", but also less natural looking.
Using frame interpolation negates the point of sending the set a 1080p/24 signal, because the set is creating frames that aren't present in the original material.
In other words, if you want to see the film as it's actually stored on the disc, you have to make sure that frame interpolation is switched off. But if you like that "live", smoother motion look, switch motion interpolation on - in which case you're no longer really seeing 24fps.
But this doesn't result in the "live" look that you referred to - that's the result of frame interpolation - i.e. "Cinemotion" or "Smooth Motion" or whatever a particular manufacturer calls it. In effect, the set is creating new frames by "guessing" what should be in between the existing frames. This creates motion that is "smoother", but also less natural looking.
Using frame interpolation negates the point of sending the set a 1080p/24 signal, because the set is creating frames that aren't present in the original material.
In other words, if you want to see the film as it's actually stored on the disc, you have to make sure that frame interpolation is switched off. But if you like that "live", smoother motion look, switch motion interpolation on - in which case you're no longer really seeing 24fps.