The Complex and Real planes as a 3 Dimensional Graph

Question

I’ve thought about this many times and have don’t quite understand it. My main question is, Why is the complex plane visualized separately from the real plane? I have this question as the complex plane has only one real axis, and most graphs are represented through 2 real axes. Though I have no idea how it would work, why can’t we take the $z$ axis of a 3D grid and make it the imaginary axis? i feel like this would allow us (assuming it would work) to see the entirety of functions like $x^2 + 1$ which only have complex solutions. I’m assuming it doesn’t work as it isn’t ever used, so why is it that it doesn’t work, and if you wanted to do something like this how would you create some kind of graph that did this effectively?