It feels like less of an expectation and more of a: the "leap" from the rationals to the reals is a far larger one than the leap from the reals to the complex numbers. The complex numbers aren't even a different cardinality.

> for us to be able to compute them all

It's that if you pick a real at random, the odds are vanishingly small that you can compute that one particular number. That large of a barrier to human knowledge is the huge leap.