Has any company ever tried being non-irrational?

I highly recommend Misbehaving by Richard Thaler, particularly the chapter of the American football draft in this instance.

If it's irrational but companies are inherently irrational then the result is the same as if it's rational and companies are rational, right? Either way you need something beside the Invisible Hand if you hope to solve the problem.

'Rational' has a specific meaning in economics; on the weak end, it means an oddly strong knowledge of probability and game theory, while at the strong end it means completely prescient.

Outside of some limited cases, such as small groups of economists, there is no evidence that anyone, anywhere, had behaved 'rationally'.

What I'm saying is that question isn't even really material to the discussion at hand. Either discrimination is rational and rational economic actors are discriminating, or else it's irrational and irrational economic actors are discriminating (or else maybe it's rational and irrational economic actors are acting rationally for irrational reasons, or whatever combination of the two you like). Either way the market will not fix the problem without intervention.