Apotrope's page

I find it funny that the people saying Wizard is fine are not even using the best example of shenanigans that Wizards can do:
Note: this is a hypothetical that is extremely unlikely to happen in real play
Universalist for up to 9 uses of Drain Bonded Item (which I just refer to as bond from here on) per day but only 3 spells/rank per day
Experimental spellshape (a surprise tool that will help us later!)
Level 8 take bond conservation now you have up to 16 (3/rank per day + 4 uses of Bond ) + 2 (additional rank 1&2 spell from bond conservation)=18 slots per day (assuming the spells you cast can generally be cast at 2 actions or less (63.7% of Arcane falls under this))
Level 9 is where things start to get interesting… you now have 19 (3/rank per day for 1-4 and 2/rank per day for 5 + 5 uses of Bond) + 4 ( 2 rank 1 spells + 1 rank 2 spell + 1 rank 3 spell all from bond conservation)=23 slots per day because we use bond conservation to get an additional use of Bond at 3rd rank which we then use bond conservation with again to get an additional use of Bond at 1st rank for 2 additional rank 1 spells per day from bond conservation.
At Level 11 you have 23 (3 rank 1-5 + 2 rank 6 + 6 uses of Bond) + 6 (2 rank 1 + 2 rank 2 + 1 rank 3 + 1 rank 4)=29 slots per day since we use bond conservation 6 times in all
Level 13 you have 27 (3 rank 1-6 + 2 rank 7 + 7 uses of Bond) + 9 ( 3 rank 1 + 2 rank 2 + 2 rank 3 + 1 rank 4 + 1 rank 5)=36 spells per day (as many as a level 18 sorcerer can cast before feats) since we use bond conservation 9 times
Level 14 you take Superior Bond and have 28 (3 rank 1-7 + 7 uses of Bond) + 12 (4 rank 1 + 2 rank 2 +3 rank 3 + 1 rank 4 + 2 rank 5) (9 from bond conservation + 3 from the combo of bond conservation and superior bond) for 40 spells per day
Level 16 you can use Experimental Spellshape to retrain bond conservation and get a different level 8 feat; also you now have 32 (3 rank 1-8 + 8 uses of bond) + 15 (3 rank 1 + 4 rank 2 + 2 rank 3 + 3 rank 4 + 1 rank 5 + 2 rank 6) = 47 spells per day
Level 19 you have 37 (3 rank 1-9 + archwizard’s Spellcraft + 9 uses of bond) + 22 (5 rank 1 + 4 rank 2 + 4 rank 3 + 3 rank 4 + 3 rank 5 + 1 rank 6 + 2 rank 7) for 59 spells per day. I probably made a mistake somewhere in here but this is pretty close to being accurate.
However you have to prepare spells that can be used in many situations as you only get to prepare 3 spells per rank. This build also becomes a lot worse when combats are ended quickly. The only area where Wizards CAN be quantifiably better than Sorcerers is in sustained combat with a gimmicky build that focuses on having prepared spells that are generally effective.

I imagine Paizo is worried about making Wizard too powerful which was a complaint about DND 5E’s Wizard since it had access to so many spells even getting access to life transference which is essentially heal with extra steps as long as you have someone else who can heal you. I think that a new version playtest for Wizard changes, maybe even multiple rule sets focusing on different solutions, would make a big difference as Paizo could see what the community at large wants and adjust the Wizard to fit that style.

(Sorry for the wall of text; TLDR at the end)
One thing of the flavor of arcane that no one has mentioned yet is the source of Arcane magic. Notably, there are very few Arcane spellcasters that come from other planes, the only ones that consistently cast arcane spells are Elementals and not even all of them that cast spells are Arcane spellcasters. This suggests that most of the Arcane tradition is more an adaptation of other traditions than its own magic, which explains its lack of unique spells and its general overlap with other traditions. Divine spells generally originate from the power of deities (usually holy/unholy deities) in one way or another, Occult spells generally originate from beings of similar power whose thought processes have, in a way, transcended the morality of holy/unholy but can also come from one’s own mind, Primal spells generally originate from the world itself and those with the ability to change the world using solely their will (the Fey), but Arcane spells do not have a clear source of power; the first Arcane spellcasters were likely dragons, all the other traditions draw their magic in part from other planes while Arcane in my opinion draws on all of these sources but as such has limited ability to do so. I’m not saying the Arcane tradition isn’t in need of improvement as I have little game experience. If, as I assume will happen, other traditions get decent spells that are on only their spell list and Arcane’s, Arcane will become a lot stronger.
Trip.H’s idea of making spell substitution a base feature for Wizard seems like it would solve many problems as it would give Wizard an edge over other prepared spellcasters and spell substitution being a part of general Wizard school makes sense given how practical of a skill it is. Since Wizard would in this theoretical be getting the ability to swap their spells around more often, would it make sense to give them three spells in their spellbook per level? They currently get up to 53 (except universalist with 44) spells known at level 20 assuming they learn 0 spells from scrolls. While some may find it a pain to manage a larger spellbook, learning 72 (or 63 for universalist) spells before scrolls would make the above changes even stronger. You could also make this change apply to Witch as the other full caster that needs to record spells.
TLDR: Arcane’s lack of unique spells is (in my opinion) thematically fitting. If we take Trip-H’s idea of making spell substitution a Wizard feature instead of a class choice, should we in this theoretical also add a 3rd spell added to spellbook per level and maybe add this extra spell per level in “spellbook” to Witch?