So instead, make non-compete clauses really unattractive for your average employee. This would include things like paying the average wage over the last year, including any bonuses (or paying the average bonuses or prorating them another way), continuing to pay benefits such as health insurance contributions so the employee doesn't pay more, and things like that. I'd even be willing to put a penalty so the company would have to pay a bit more if their pay rate doesn't meet the industry standard in the area.

You could require them to mention it, but that's just a more complicated version of banning it outright.

The difference is the matter of liability. In the regulation case, a business found to be in arrears could be hit with a very large judgement. On the other hand, if non-competes were simply banned and employees were unaware of the law, they could still suffer under the chilling effect of an unenforceable clause in their contract. To then discover the problem later and show damages in court would be much more difficult.