Except everything I was talking about were mechanics, they are just mechanics that you now evidently pretend are never actually used.
I have, in fact! And I've had Wizard players who play the game as written, as novel as that apparently sounds to you. I've had a Wizard and a Sorcerer in the same party (same race too!) and they could not have played more differently. And this was at launch, no less!
What you appear to be describing are players who'd prefer to be playing Sorcerers but don't, presumably because of (both real and perceived) balance issues. And I'll be the first to admit that Sorcerers are unbalanced compared to Wizards, but that's not an issue of class identity.
Your argument was that the classes were designed to have no meaningful mechanical differences in identity. This is evidently false, and a course correction to "but no one actually plays it that way!" changes nothing in that regard.
I will, of course, never say no to changes that make those differences even more evident. A more meaningfully different spell list would be a great place to start, honestly. Something like the Bard's spell secrets would be perfect, honestly.