No, they didn't "replace" the roleplay restrictions. They just threw them out. They were not serving as a balancing feature at all. What happened was that, either you followed this very specific style of play, or you couldn't use the class. If you did follow the style, and built your OOC concept around it, there was zero restrictions and you could do whatever you wanted anyways.
Furthermore, these roleplay restrictions were often used as a cludge by a number of GMs to engage in punishing players rather than providing stories or balance. Therefore, it was removed.
What the cantrips replaced were the greater number of level 1+ spells a caster could use per day. That's where the balance comes into play. 5e Spellcasters can cast less non-cantrip spells per day than any other edition, irrc. But they can still cast cantrips, so they still feel magical instead of needing to rely on crossbows or whatever when they run out of spells per day. No one liked playing a wizard who had to pull out darts or a crossbow. Well, there might have been, but they're generally the minority now. That is where the balancing comes into play.
That's not what I could call good role play restriction. By that standard, I could never play a ranger that owned a house where his family lived. You can't have a war plot with Rangers serving as the military scouts, since technically they'd have a company of them traveling together. Which is all kinds of meaningless restrictions that get in the way of stories.
