Even for an almost fully digital synth like the DX7 a bit-accurate emulation is difficult (there is a rich discussion of this in one of the other threads here). For analog synthesizers, there is a lot of character and nuance in the individual circuits that are difficult to capture in a digital model, across all possible configurations. In the mix of a full song though, its not often that people can notice the difference.
Aliasing--the introduction of extra unwanted and generally non-harmonic frequencies--is also really hard to avoid in digital systems. For more esoteric instruments like Eurorack modules or Moog modular synthesizers, the physical interface is an integral part of the instrument--software versions of these exist but are obviously very different to interact with using a mouse or touchscreen.
> Why aren’t all new keyboards (or those other things DJs have on stage) simply software, maybe with a custom input device for easier live use?
For live use this is very common nowadays, though physical single purpose keyboards (even fully digital ones) still are used widely. In a fast moving stage show you may not want to mess around with the complexity of a full personal computer setup. In modern operating systems, even with 100s of processes competing for CPU time, real-time audio may rarely drop out (the result of which is audible clicks and pops), but even this is too risky for a big professional live show.