I know this thread is for people who think the Sorcerer is flawed, but I can't help but butt in. I agree that the Sorcerer appears to be less potent than the Wizard.
What's unfair is that this isn't true.
The Sorcerer requires thought and strategy, whereas the Wizard doesn't. You have to look through each Sorcerer spell and see whether each metamagic will be useful. The Wizard's powers are self-evident, with little ambiguity. The Sorcerer gives vague rules and hopes the player will discover some powerful combination. It requires some rules lawyering and a DM who knows the class.
This is my only problem. The Sorcerer isn't as simple as the others and so it's seen as unbalanced.
The lack of spells is necessary for separating them from other classes, especially wizards.
'Can you be comfortable with such a small spell-list?' Y/N?
Otherwise: Multiclass/Pick Another Class/Take a feat
It's not so much the lack of spells but the lack of variety. The Wizard has flavourful spells like Conjure Elemental, True Polymorph, Nystul's Aura, etc.
The Wish spell can compensate for a lot of the more potent spells, being able to metamagic them, makes them better (Divine word, extended to 60ft/ Subtle Mass Suggestion).
The Sorcerer's Font of Magic, the 1-20, is equal or even better than arcane recovery because you can design your own spell slot arrangement. You're not confined to the 4/3/3/3/3 slot arrangement for 1-5th level spells. You could go 37/0/0/0/0 - or 0/24/0/0/0 - or 0/0/14/0/0 - or 0/0/0/12/0 - or 0/0/0/0/10 with over 20 Sorcery points to spend on metamagic or lower slots.
If you're going to compare the Sorcerer to a superior Class, compare them to the Cleric, not the Wizard. Clerics have a bit of everything: D8 hit die, healing, radiant damage, martial ability, powerful smiting, Divine Intervention, A list of bonus spells, a powerful short rest ability capable of destroying undead.