In DSP you can just add bit-width (trading speed, power, area) and get any
precision you like, with accuracy limited only by the input SNR.
In analog every stage has a noise contribution, as well as built-in errors of
some size (designed against but never zero). Against a fixed voltage headroom
and a likely lesser common-mode range, this presents a fundamental dynamic
range (differential voltage range being 2*VDD, max, against an equivalent
noise and error voltage sum) limit.
Of course similarly to DSP, you can improve the noise and error terms at the
cost of area, speed, power, complexity. But there is more of a "wall" (or a
hill of ever-increasing slope) that simply throwing gates at the problem,
will not get you over.
On the other hand I see people trying to read a thermocouple with 24-bit
ADCs and wonder if they really understand what matters.