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The “scratch” card brought into play by “Terminate the Tower” doesn’t seem to have the same effect of increasing in value when more scratch cards are played.

They do, but it only buffs Scratches that have already been created. 

So a brand new Scratch created by Terminate the Tower will start with 3 damage, but will increase the damage of all currently existing Scratches by 2. 

Ah, interesting. I was expecting the buff to be “buff any future Scratch you use” rather than being attached to specific cards.

Is that an intentional design choice? Would it affect game balance to do otherwise?

It's intentional since it is the same way that Claw card in Slay the Spire (the reference for this card) works!