If this became common - or was known to be common - it would lead to interesting fake-outs.I've only experienced this on the player side, but usually neither I as DM nor the DMs I have had speak in spell names when describing the action. It might be "It gestures and three bolts of force fly out striking Gumar in the chest." but generally not "it casts magic missile, three bolts, all at Gumar." But that would be completely normal on the PC end to communicate to the DM your action "I cast magic missile, three bolts all at the hag."
In my last game I had it and once I got used to using it I would just fling it the first time an enemy caster started to cast. The first couple games after my wizard got it I kept cursing myself as only remembering I could use it after the fight was over and we had been pummeled with spells.
So once I got the rhythm of it the games would usually go "The hag casts a spe-" "Counterspell!"
A mage encountering another mage would know that that mage would counterspell immediately so would throw out a 1st level spell to make that mage waste a higher level slot.
Of course the counterspelling mage would know that the other mage would know and might cast a lower level slot so might wait.
Of course the casting mage would know that the counterspelling mage would know... and my head is starting to hurt.
Realistically though - an action is generally worth more than a reaction. So counterspelling the mages first spell, even if it's lower level is worth it - due to the action economy. Of course it's then also worth the casting mage countering the counterspell (which he suspects is a counterspell because it's unlikely to be anything else, though it could be) with his own reaction to preserve his action economy - and my head is starting to hurt again.