I really don't believe that using approximations of real numbers is going to be the bottleneck for AGI.
I'm not sure that makes any difference (in either direction).
I mean, at the scale we care most about, the universe appears to be continuous, so an AGI has to be able to tackle continuous-appearing problems and use continuous-appearing representations.
OTOH, the universe is likely to actually be discrete, so an AGI has to be able to tackle actually-discrete problems, and use representations that are actually-discrete on a fundamental level.
There isn't much of a contradiction between these constraints, although the prospect of a continuous-appearing universe that is actually running on a discrete substrate seems to give a lot of people a brain cramp, and that same brain cramp gets elevated into 'proof' that current approaches cannot lead to AGI. Which is nonsense (there may be other limitations inherent in current approaches, but that can't be one of them).
One might as well claim that computers are digital and brains are analog and conclude that digital image representations cannot possibly be used to communicate information to analog brains.