I'm still not convinced it does. The wording of the spell seems to strongly indicate the damage is part of the same attack, and therefore doubling of damage dice on a crit would still apply.
As you hit the target, your strike glows with divine power.
The target takes an extra 2d8 Radiant damage from the attack.
However, as a bonus action and a spell, you're limited to one Divine Smite per turn. Our current campaign, the paladin, who often is hasted, frequently gets two or three smites in on their turn. That's the real nerf, and I'm fine with it.