Spellcasters are already vastly more powerful than non-spellcasters, and you are worsening that gap in the system. I'm not sure this counts as a balance issue, because it's already a problem to such a degree that non-spellcasting classes generally can't compete with spellcasters even at level 1.
However, some classes-- the ranger in particular-- have incredibly powerful exclusive spells (like Instant Enemy) that are even more powerful for full-casting classes like the Wizard and Cleric, who get slots of the required level much, much sooner. This change will make all partial-casting classes worthless, since access to other classes' low-level abilities later in the game cannot possibly make up for those classes gaining your late-game abilities early in the game.
The inclusion of psychic spellcasters like the Occultist would be additionally problematic: the Occultist is usually limited by an extremely small list of spells, but now has access to all spells ever (additionally problematic since this presumably trumps the Occultist's school restrictions).
Sin Magic Specialists get a huge bonus, as their 'prohibited schools' penalty shtick no longer inhibits them in any way, and they essentially get +2 spell slots of each level. They still are some of the worst schools when played straight; lacking school abilities.
Depending on the Spells Known feature, I'm guessing Clerics are going to be (relatively) nerfed, pushing Wizards solidly ahead in terms of class ratings. If the Spells Known feature gives Clerics a number of spells known at each spell level equal to the number of spells on the currently existing Cleric spell list, however, the Cleric will remain about as good as the Wizard.
I think the classes most benefited by this change, however, are the Witch and the Shaman, who ordinarily get awesome powers in exchange for a sucky spell list. The extra spells aspect of Patrons no longer makes sense, of course, but having full casting, occasional early entry into some spells, and extra abilities the regular full-casters don't get put these classes up to t1 in my opinion, under the new rules. Particularly the Witch, who, like the Wizard, can add spells to her familiar with loose change (especially if you, like you say in the question, only increase the cost of learning new spells for wizards specifically)
I don't know if you count Alchemist stuff as spells, but if you do, there are going to be a lot of weird consequences with extracts and stuff of spells you can't normally make it that form.
Ultimately, though, your system doesn't meet your title:
This isn't "all classes can cast all spells". This is "full casting classes can cast all spells". Rangers will still only ever get up to 4th level spells, Summoners 6th, Fighters none, etc. This is mostly a massive worsening of already existing tier issues, with some slight reordering on the side.