First, if something is a "counterplay", it shouldn't matter if it's a role countering another or a spell countering another spell. Counters are counters, we can't have double standards here.
A role can be better against other roles and that's fine.
But a role can't literally counter another role, as some well performed actions may do.
That's why most roles only soft-counter one another.
So you might say a champion. who has a 55% winrate over another is a "counter", but it isn't the same way actions can negate another action and still be healthy.
Second, what's so hard about clicking your ally?
Timing. Awareness. If you click too late your ally already has taken the damage and the shield is wasted. If you click too early the enemy can choose not to use his cooldown, wait till the shield is down and then go in.
Even if the shield doesn't get hit, you can just walk away until it's up again.
If the aggressor has to back off because there is a shield he has missjudged that it's up, he has missjudged his power in bursting through and/or the shield has done its job. That's why you engage when key abilities are down. That's why new Zed players blow up when moving into the enemy team, because they didn't let their tank eat most of the CC first.
So, the likely scenario will just be both the back line and the guy looking to dive it sitting out of a fight completely.
If the backline never has to use cooldowns, then yes. But if the enemy team can win the frontline fight without using any cooldowns the game is pretty much over anyways.
It's just stat check, plain and simple.
That's a problem with shields, yes.
And one of the reasons Karma flip-flops into and out of relevancy ever since they took the damage away from her RE; if the only thing a shield (or shielding character) does is shielding, then he will be oppressive if good, and useless if behind. But gladly most shields do more than just shield and most supports do more than just shield. It's just one of the reactionary actions they have at their disposal, next to some CC.
A dive has to be made during the split second between the enemy wasting a CD/droping below your kill threshold, and realizing that you can kill him now.
That's why longer cooldowns for defensive actions - such as shields - makes sense. As a game designer you need to create windows of opportunity for divers/assassins. I am just opposed to calling this dive a "reaction" since it makes talking about shields and counter-actions a bit confusing.