If I, as a DM, have an NPC with Counterspell prepared, first and foremost, I’m going to stay out of melee as much as possible, letting my goons engage. And then I’m going to use my Counterspells on the guys in robes or waving their holy symbols around who are able to cast ranged and/or area effect spells my way.
Very rarely would I focus on the guy in plate mail casting spells immediately upon landing an attack, because that should be extremely obvious that he’s just casting smite, Xanathars rules aside.
Only if the paladin were hitting the Counterspelling NPC themselves would they cast it as a form of self-preservation. By that point the party should be aware the NPC has Counterspell, so it becomes a tactical decision of when to cast spells, or try and get the NPC to use it on something else first in the round.
That said, the PCs might fight an NPC that could logically have Counterspell on their list maybe one in ten encounters, because not every NPC is an arcane caster.
Also, it’s boring. Magic in combat should be used by the GM to create interesting situations and obstacles for the PCs, and they should vary encounter to encounter. Using the same tactic all the time can lead to dull fights and frustrated players.
It’s simply not common enough, at least in games I’ve run and played in, to warrant consideration as a downside to making Divine Smite a spell. Same with silence, which, as an area effect, can hose ally casters as much as the enemy in combat.