It's not that wizard is incapable of dong nothing. It can do things!
The problem is that even support wise, with the way cleric domains work, they are just... better. Take magic domain for instance. Greater dispelling once per minute. Starting at level 10. In order to do this as a wizard, I need to be level 15. But then also, I need to give up all conjuration magic. It gives the cleric so many spells that wizards would use and want. Sure. Not greater breach or mords. But at the same time it gives mantles. Mage armor. A bonus language. Additional spell craft and crafting points. A free scribe feat (Or possibly craft wand depending)
A single domain of which you get two, negates many benefits of being a wizard. As that same cleric can also use the same summons, gets access to undead sooner than you do as a wizard, has far -far- better buffs, can heal, and has much more versatility. And you can do this (Minus the summoning) as a war priest, and hit 56 AB while doing so. Still having all the absurd buffs you'd want and as much damage as a weapon master with elemental avatar meaning you drop 3 AC.
Cloistered can spam all sorts of spells linked to domains almost non-stop. Far more powerful ones than a wizard can.
Healer/Defiler will keep everything alive or murder it and can still use anything they want summon wise. They don't get armor. Sure. But they can still give +15 AC as a minimum. 19 with haste. Or literally upwards of +25 AC if they have the right domains which also offer insane other value and power.
Most cleric paths give additional power with minimal, if any, downside to them.
Warlocks depending on their pact can infinicast boatloads of damage, boatloads of CC, and eldritch blast is no joke. They have so much versatility with how you can make them, and don't even need to rely on DC's to be consistent with what they do.
Favoured souls have some boons but I feel like are just worse versions of clerics now (I know this isn't 100% true, I just feel like domains now give so much power and so much path benefits that favoured soul which had a super cool niche of being an ultimate battle-cleric adjacent thing is now lacking).
Shamans have some neat build paths with barbarians, bards, rangers, and can be really interesting casters or melee-esc builds, or even a full on pokemon trainer with elemental swarm, animal empathy, and 2 tribals where you send an entire army after people.
Elementalists/Hemomancers just obliterate things. They even still have some minor supports.
Bards who are support still give -massive- buffs to a group unable to be achieved by any other means both in and out of battle. God forbid it's a dirge bard where you can burst reliably for like 400 damage, giving even more insane buffs, and crippling debuffs while still getting full bardsong and mummy dust.
Druids have interesting spells but are encroached on now by clerics and shamans. I feel like they are good due to the fact that totem exists despite the intrinsic issues with the stat hits up front and early. But the wildshapes and interesting spell list at least gives it something that stands apart from its peers.
Wildmage is interesting and has power, but still often relies on DC's for it to be effective. It falls into the same issue that the rest of wizard does.
Shadowmage giving shadowdancer capabilities is one of the biggest jokes I've seen in the universe and should be actually deleted or reworked entirely because it suggests something might be viable but it's probably one of the biggest mistakes I could ever envision somebody making. Maybe if you're going to be a VERY specific palemaster or necromancer focused character or have some other small benefits it might hold a more capable spot. The RP of it is neat! But you're trading flavour for a boatload of power and usefulness being tossed out the window.
Also we have transmutation specialist wizards at home. It's called Spellsword. I cannot fathom a world where anyone plays this for anything other than RP, and it still being bad compared to a spellsword.
But yes. I could write up a document for sorceror bloodlines/synergies.
Could even write up some ideas around wizard.
Arcane trickster - Assassin/rogue/shadowdancer synergies.
We have arcane archer. It's honestly not a terrible idea at all.
Maybe some kind of crafting variant, that allows it to make things better. Might not be super optimal for PVP/PVE but it gives neat support variations. Maybe it can make stronger/more interesting golems or support creatures only it can use but it has to invest in them in meaningful ways.
Some kind of mystic theurge.
Some kind of summoner class, that has to invest additional feats in creating a custom creature that it can use like an Eidolon rather than a familiar.
Shadowcaster rather than the shadowmage we have now. Have this maybe gain power as people around them use spells, or as they use spells. Shadow magic is the null that exists when other magic is used and the reflection of those. As magic happens around you, gain points towards special abilities and themed powers.
Truenamer: Have 120 WPM (Or just like to use the NUI bars like bards do?) Type your magics. Cast spells empowered by having to use words and emotes in the middle of a fight.
Obviously some of these wouldn't work, wouldn't be interesting and need actual design docs. Yes, I know technically many of these are other classes or PRC's. All I mean to suggest is that there's so many ways you could do wizards more interestingly with say, magical theses/archtypes.
But I feel like the only thing that'd 'fix' DC spells in almost any capacity is going to be a shift to a PF2E system where spells have a range of effects.
Usually it's something like. They fail a DC by 10 or more? Extra effect. Fail the DC? The normal spell. They save? A much lesser effect. They save by 10 or more? Nothing.
I don't know. It just feels like as it is now these classes are so in the dust they may as well be under ground.