Three points.
1) Being able to change your entire list of spells prepared is still a stronger option than being able to change a single spell.
2) The wizard spell list is still much stronger than the sorcerer spell list. Factoring in PHB and XGtE, it's 296 spells to 188. And a lot of those spells are good.
3) The amount of spells in a spellbook is only limited by access, money, and time. All things that are under the purview of the DM. Like most things in 5e, the balance of sorcerer versus wizard is going to be strictly dependent on the DM's playstyle.
Point 1: Agreed, partially. Know any mage that has his entire spell list from the begining? No? I thought so. With enough long rest, the sorcerer now has a full access.
Point 2: Ho... Versatility is supposed to be on the side of the wizard. But still, full cleric's list with the right subclass? At no cost but a simple long rest?
Point 3: Yes and no. At the base core, the wizard to have access to the full spell list will need both a lot of money and time. Two things that in any game save Monty Haul you'll never see. Never, ever.
I...don't know? I wasn't quoting you.
Edit: Personally, if it's really a point of contention in a game, I'd just let wizard put any spell in the game in their spellbook, assuming they find a scroll (or some other source) for it. It gives wizards a cool niche.
Very generous of your part, but this changes nothing. The wizard still has to find the spell and not the sorcerer or warlock. They only have to sleep it through...
There is a reason why the arcane spell list is either limited (sorcerer and warlock) or hard to obtain (wizard). Having everything available at a moment's notice is in the long run, quite unbalancing. If I don't want a wizard to have wizard eye, it is easy. The wizard either don't find or must sacrifice one of his "spell choice" on leveling up. There is a cost. The same for the sorcerer, warlock, eldritch knight and arcane trickster. With this rule, there is no cost but a simple rest. All the spells in the world for the cost of a sweet dream. A caster's dream come true!
Note: I am the one who complains that I don't see enough sorcerer and warlocks in my games because people really like the wizard's versatility. At the same time, this rule will make wizards almost non-existent in the long run. This is simply too good, way too good.