Half Caster spells are equal in number to the Sorcerer, while all the other full casters far exceed the Sorcerer.
I initially thought that the Warlock shared the same limitations, but then realized I was mistaken.
The Warlock has 15 known spells. Through Mystic Arcanum, they gain 1 additional spell of 6th, 7th, 8th, and 9th level for an additional 4 spells. Then through Invocations, they could gain at will usage of 11 spells and once per long rest of 7 spells.
In total they have potentially 37 spells available to them based on the Invocations selected. Yes they have 4 spell slots for spells at 5th level, but they regain them after a short rest.
So why the strict limitation on the Sorcerer?
There really needs to be a couple of specifically "wild" spells that cater to the image of the Wild Mage.
Not asking for many; as little as three would probably suffice (one level 1 spell, one level 3 spell, and one high-level spell would do it).
These spells should default to chaotic random results, but allow the wild mage to get better results (thanks to the subclass abilities).
At least the third level spell should be damage-dealing spell with an attack roll, rather than the target saving.
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As for the Draconic subclass, it's better off, so I really don't think it absolutely must have any unique spells. But since there are dragon spellcasting supplements for previous editions, it should be easy to find the same number of unique additions to that subclass.
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Note: I'm not even asking that these spells get added as bonus spells(although that would be nice, wouldn't it?).
Just having them on the spell list is the minimal nod I'm asking for.
(Meaning that all Wild Mages won't take all the "wild" spells, just like you don't have to take Confusion, arguably the "wildest" standard spell. For example)
I've recent;y created a wild mage for an upcoming game, and my DM converted the wild magic spells from the old 2e Tome of Magic books. Better still, she's giving them to my character as bonus spells.
Perhaps take a look at that book, if you can find it. It has fun stuff.