"There's a line of thought which assumes that an employee that's given notice has already mentally "checked out". Therefore, it's unwise to present counteroffers"

That's just bullshit rationalization why they don't want to raise pay. Profits come first for most modern companies, and the rationale for action trickles down from that basic driving force.

Best engineers are coin operated and problem focused. If they get an offer, say, 20% better than their current package with the roughly same job otherwise, they would be blind fools not to leave. Talking in the general Big Co. environment, that is. In smaller companies with stronger ties other dynamics might kick in.

And, there is the situation of the gimme-more-money-or-I'm-gone bluff, of course.

I don't think there is any rational reason not to give a counteroffer to a solid contributor - if the offer is real and he's worth it. Political reasons might of course kick in, like a corporate policy, that have nothing to do with the individual contributors motivation or output.