I don't think the right way to look at it is from the "counter-offer" perspective. It frames it as adversarial and between you and the team-members, between your company and others. It also makes it "reactionary" as in a reaction to something external.
It is similar to someone exclusive and married telling their spouse: "if there's someone else out there courting you and you're considering leaving me, tell me and I'll match their offer and take better care of you".
It sets the wrong incentives and makes the care, the offer, conditional to another offer from a third party. A better clause would be one that explicitly unhibits conversations about compensation, future, careers, equity, but that should not be conditional to anything, or counter to anything. It should be "we can talk about pretty much everything here".
I think an alternative is to act from within and make your offers neither conditional to anything, except the company's finances, nor counter to anything except to your own offer. I think that showing the intent and the willingness to act from within with your actions day in and day out is better: you value and respect the people enough that you will generally do right by them throughout the relationship, that will not necessarily end with their departure, within the constraints of the company that will generally be shared. That means that your actions will make them trust you enough that they will know they're not being screwd. They'll know that you will, within your means, spontaneously bump their compensation without them even asking.
A sequence of spontaneous bumps as the company picks up steam goes a long way.
Talking, probing, observing, sensing. You're amongst colleagues. They'll share how they view things, what they want to do, what their constraints are. Doing the right thing every time, or trying, goes a long way.
Many of the problems result from information asymmetry and people's imagination. Imagining they're left behind or missing out on something or being dealt a bad hand. Your actions every day puts their mind at ease.
Building an organization where compensation is not the only factor people are choosing to stay for, even though it is important, is important. In other words people who leave an organization for just a marginal incrase in compensation is symptomatic of deeper problems. While building this, actions day to day speak louder, and doing right by the people is more effective than adding a clause that sets the wrong incentives.