First they tried to fold the sorcerer, warlock, and artificer into the wizard during the playtest.
The community reacted very negatively.
Then there was the playtest sorcerer that turned into a fighter when its spells ran out.
The community reacted very negatively. Many thought the idea was cool but not for the sorcerer.
And innovation was stifled in 5th edition. After all the backlash, the designers quit trying to add big changes and opted for little one and variant. Then the wizard favoritism took hold.
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Just look at it. For all the desire for the sorcerer to be different, being a variant wizard is winning followed by thematic shooter of spells.
I don't think many sorcerer fans think the same as you when we voted "natural wizard" (I voted as in "should have the same potential and kind of effects as the wizard"), maybe it should have its own poll.
But you told the story backwards, the sorcerer was there first, and the welcome was warm, with a lot of caution because it didn't allow for conversion of previous PCs, but the transformation effects were confined to the subclass and a different one would have helped more. I think that another try with two more subclasses would have satisfied sorcerer players, and led to a good sorcerer with at least three feedback cycles -the current one had 0 of those-.
The problem was that it was a little over the top, maybe too much for traditionalists -full caster with martial weapons and heavy armor!-, almost like trolling. Then all wizard players started making an uproar and demanding "more toys now" without having to lower themselves to use an "inferior" class. Then Mearls and Co decided to make the wizard eat them all, and wasted their time with that, and then there was an uproar.
I like the idea that the Sorcerer has a natural connection to magic. Where the Wizard has learned the code-words to unlock the tools to shaping reality, the Sorcerer has an innate connection to the magical energy surrounding them. Maybe it's from simple luck of the draw, maybe it's from genetics. I like to conceptualize the Sorcerer similar to the "spark" of a Planeswalker from MTG. Some people have it, some people don't. I do think that the Sorcerer has a theme, I don't think that theme should be limited "blaster" but I do think they should be limited to a particular theme, like the Eldritch Knight is limited to a theam that makes him more of a war caster with an array of offensive spells instead of utility.
I think this could be filled in through the bloodlines. Fey bloodlines could be more about illusion and mind effects. Old One bloodlines could be about crazy stuff. I think there's a lot of room there, but it certainly takes up a LOT of writeup space.
I have one system for that, I tried to make an expression for 5e, but I haven't finished all spells needed. This was an idea I had for a story, were witches -sorcerers- and their magic were divided on five different types.
Affinity.- Have a connection with an element -a thing- you can control it, shape it, summon it, etc. It can be from the classical Fire and Ice, to more mundane things like clothing.
Manipulation.- Controlling physical things and objects -but also animals and people like puppets.
Creation.- Being able to use magic to creates things of any kind|.
Alteration.- Being able to transform things, and to change their properties.
Dreaming.- Things like emotions, share dreams, illusions, enter into minds, etc. In other words control of non-physical things.
Each witch belongs to one category, they can use magic from that category at their full potential, they can use magic from other categories, but it is harder the more different it is, for example creators have problems manipulating things and viceversa. Witches with an affinity have the least potential to use any kind of magic different from their own, even to use their magic on something they aren't attuned to, but they have a way easier time doing it, so they are the most common kind of witch. So they as a whole have an unlimited potential to do anything, but each individual one has a theme.