Why not? Everything you can do with complex numbers, you can also do without them - they just make things easier.
By pushing the common complexity into a shared location, problems become easier to solve. Complex numbers really do factor out a lot of the complexity from many problems, at comparatively little cost.
When people say they don't "get" complex numbers, usually they mean they've seen them mentioned, but have never actually done anything with them.
It's like staying that you've read a book on lisp and don't get it. Using these things is an essential part of coming to understand them.
What people complain about is that they do not have a (real or hypothetical) device which can display its measurements as a complex number while they do have devices which measure properties in terms of integer, rational and real numbers.
Even if real numbers are "real", only a countable number of them are computable, even in theory. The rest are probably completely inaccessible, barring hypercomputation. (Interestingly, access to true real numbers gives you hypercomputation as a side-effect)