...what exactly is needed to make a system sound live
A reasonable simulation would be very low noise floor & very high dynamics...
...but, OTOH, I don't expect a system to sound like live music. Live music would not be my reference (as it isn't yours). Rather, reproducing the medium would be a better /more reliable and palpable reference point.
In the rare cases where a reproduction is such that it creates spontaneous involvement, there is some magic. Sometimes, when the Gods are smiling, there is a lot of energy coming out of my spkrs (relatively speaking, of course) and the effect of a live recording (even average recordings) is lovely.