In a way that's technically true, because solving ill-conditioned problems with noisy data is both difficult and the results are often meaningless. But you almost always have some choice about which of a multitude of subproblems you try and solve to reach your actual goal. It's like the difference between executing an algorithm and designing an algorithm. So instead of solving ill-conditioned subproblems, you spend your effort getting to well-conditioned subproblems instead.

I think a common example of an ill-conditioned problem that's too annoying to solve is weather prediction past 2 weeks in advance, because it's a chaotic system, so I don't think what you're saying is wrong.