Do you realize it could cost a wizard over 50,000 gp to be able to have access to every spell in their spell list?
Yes, and I realize that this beside the point and isn't an issue if you actually compare the sorcerer and wizard and what they both get:
To recap, sorcerers have a number of spells known (of a level they can cast) equal to their sorcerer level + 1 (until 11th-level, after which they gain 1 addition spell known every other level). Wizards, on the other hand, can prepare a number of spells from their spellbook equal to their wizard level plus their Int modifier (with a minimum of 1). Their spellbook contains, at 1st-level, 6 1st-level spells plus two spells of any level they can cast at each additional level.
Here’s a quick comparison to see how this looks at various levels:
Level 1
The sorcerer has 2 spells known. The wizard can prepare 3 spells (assuming a 14-15 Int) and has 6 spells in their spellbook (all 6 being 1st-level spells).
Level 5
The sorcerer has 6 spells known. The wizard can prepare 7 spells (assuming a 14-15 Int) and has 14 spells in their spellbook (assuming they don’t purchase, discover, or research additional spells to add to their spellbook)—assuming they always pick the highest-level spells available to them, this would be 8 1st-level, 4 2nd-level, and 2 3rd-level spells).
Level 10
The sorcerer has 11 spells known. The wizard can prepare 12 spells (assuming a 14-15 Int) and has 24 spells in their spellbook (assuming they don’t purchase, discover, or research additional spells to add to their spellbook)—assuming they always pick the highest-level spells available to them, this would be 8 1st-level, 4 2nd-level, 4 3rd-level, 4 4th-level, and 4 5th-level spells).
Level 15
The sorcerer has 14 spells known. The wizard can prepare 17 spells (assuming a 14-15 Int) and has 34 spells in their spellbook (assuming they don’t purchase, discover, or research additional spells to add to their spellbook)—assuming they always pick the highest-level spells available to them, this would be 8 1st-level, 4 2nd-level, 4 3rd-level, 4 4th-level, 4 5th-level, 4 6th-level, 4 7th-level, and 2 8th-level spells).
Level 20
The sorcerer has 15 spells known. The wizard can prepare 22 spells (assuming a 14-15 Int) and has 44 spells in their spellbook (assuming they don’t purchase, discover, or research additional spells to add to their spellbook)—assuming they always pick the highest-level spells available to them, this would be 8 1st-level, 4 2nd-level, 4 3rd-level, 4 4th-level, 4 5th-level, 4 6th-level, 4 7th-level, 4 8th-level, and 8 9th-level spells).
With this optional rule, the sorcerer can trade out one of their known spells per long rest while the wizard can trade out all of their prepared spells during the same. Also, sorcerers can choose to trade out this one known spell from their entire spell list (which is rather smaller than the wizard's spell list, for what it's worth) while wizards can change out the entirety of their prepared spells from a more limited list in their spellbook (while still having more spells prepared than the socerer's available known spells).
So, no, I'm not seeing how this is in any way overpowered or gamebreaking.