> I understand a lot of it was a top-down change driven by converted emperors like Constantine

No, it was actually driven from the bottom up, as many people converted due to the appeal of a universal savior regardless social class. Christianity however was just one of the many death cults around during that time (meaning they are concerned with offering salvation when you die) such as Mithras or Isis worship.

Constantine legalized it because it was already so popular, especially among the upper classes, that would've been strange to continue to pretend it doesn't exist. The story of his conversion where he saw a cross in the sky and painted the (chi rho, first two letters of Christ in Greek) symbol is likely untrue and just a form of state propaganda.