Wrathful Smite is only d6/ level vs 2d8 a real smite.
You also need to blow a feat on it. Paladins and Rangers get that free so opportunity cost they've picked up GWM as well plus smite/HM or both if you're an avenger.
Wrathful Smite is only 1d6 with a 1st level slot, but you have both higher level slots and more slots than a Paladin of equal level, and you are getting cantrip scaling for one attack on top of that. At high level a Bladesinger is also adding Intelligence damage to every attack on top of that while in Bladesong. You do use a feat for it.
GWM is more damage if you are using a heavy weapon, but not more damage if you are not. Further it is available to those casters as well (although not really compatible with Bladesong).