It's no more or less a good analogy than any other numerical or computational algorithm.

They're a fixed precision format. That doesn't mean they're ambiguous. They can be used ambiguously, but it isn't inevitable. Tools like interval arithmetic can mitigate this to a considerable extent.

Representing a number like pi to arbitrary precision isn't the purpose of a fixed precision format like IEEE754. It can be used to represent, say, 16 digits of pi, which is used to great effect in something like a discrete Fourier transform or many other scientific computations.