Are you going to do a chemical test of their hair and body surface too?

To be totally clear, you could do this, but it's going to start an arms race of trickery.

The ancient Greeks had olympic athletes compete nude as a check against cheating.

You’re escalating just a bit from “hey, you got any gunk on your hat, head, mitt?”

Watch an MMA match. It takes all of five seconds for a ref to run their hands over the competitors head, hands, etc.

Which is certainly better than… nothing.

It is better than nothing. But you've also got people going on and off the field frequently and a strong incentive to cheat. If your five second check is circumvented it's no longer that much better than nothing.