To be clear, I am not talking about game mechanics. Just the concept. If you learn magic from study and research in my view / world - that makes you a wizard. It is what defines wizards.
Again, I am not talking about mechanics. I agree that size of list has nothing to do with. However, I think it makes sense for the flavor of sorcerer to have a more narrow focus of magic types, but more variability with that type. For instance, I would love a dragon sorcerer to pick an dragon ancestry, so I sorcerer with red dragon blood would cast only (or almost only) fire magic, but be able to use metamagic or whatever to cast more variations of fire magic (change the shape, range, targets, damage, etc). If feel like there is a lot fiction that supports this type of innate ability restriction. In fact, I think there is more support for something like this than the generalized D&D wizard.
I agree for a wizard, I just don't agree for warlocks and sorcerers. In my view they use magic completely differently. I want my classes to be distinct, not more of the same.