i agree there should be a blank slate for each character. since youre right it could ruin peoples backstories etc. But BG3 already breaks the pre-story blank slate by having background stories like "Noble" etc.
That doesn't break anything. It's a part of D&D system and the full list of backgrounds pretty much cover whom you possibly can be in Faerun in very broad terms. Same Noble background doesn't tie your character to any particular lineage and doesn't define how much of a proper noble life you had in your life. Your suggested scenarios are actually placing characters in very particular circumstances in which they probably never was by some backstories.
Previously I suggested to add another tutorial level with literal normal day where we could define connections to some NPCs by player choice. A normal day is something that happens to everyone, so the final goal of your suggestion could work with that, but not a particular class-based scenario.