I propagate it for game theory reasons. If people can be counteroffered easily there is no incentive for employers to give raises of their own accord, they can just wait until you have another offer in hand.

This. It's not about losing the job, it's about you just showed they don't need to offer raises to keep you.

Wouldn’t employers be incentivized to give raises as soon as it was more cost efficient than counter offers?

Probably.

I was told by a manager that HR has a difficult time figuring out salary levels for tech skills. And that an in-hand offer is very effective at convincing them, and upper management to approve a larger than normal pay increase. Worst case, they might just tell me to take it.

I suspect some of "stay is bad" also comes from the employer end... even if you match an offer, is that employee likely to keep looking? They were unhappy enough to start looking - was compensation the only thing that bothered them? Probably not. May as well let them leave on their own, on good terms, and get a replacement ASAP.

If that were the case, would they stay for the money when they already have the open door and the money at the new place? Most of the best employee's I've worked with interview regularly. If I managed such employees, I wouldn't consider it abnormal for them to do so.

I expect my employees to look and interview. But, at some point, if somebody keeps coming back for counters, maybe it's time to let them go peacefully? Not sure, never had somebody do that to me, but have seen it on other teams.