Well first off, 20th level is always hard to balance. Also the DM that allows a x5 daily use of wish is either a loon or is smiling the smile of one who knows the devil is in the details.
IF you start using wish spells too much(and I don't know how it would be allowed in most games), you'll draw the attention of various very powerful beings who won't like the threat you pose to the order of things.
You'll get perma-killed.
Its been said...but I figure I'll say it anyway...
20th level is really hard to balance. The characters are all going to be more powerful than most of the game world. Really frigging old dragons, borderline deity like engines of the destruction (Terrasque, I'm looking at you...yes...you), and the most powerful non-named demons/devils/celestial beings are the kinds of monsters it takes to challenge them...and even then, using them as written tends to only challenge part of the party.
And...since your talking about a magic item...you cn always follow the golden rule...the DM can always veto soemthing, or change how its made ect.
It also helps to actually read the limitations on the base item itself. Staves can only hold 10 charges. Recharging a charge takes a spell slot equal to the highest level spell in it, and can be done once per day.
I think that this might be more of the issue of putting wish on a charged item. It is a powerful spell, and if you put it on a item to be cast a lot, there are going to be significant effects in your game.
I'm starting a 20th level PF game, and was talking with another player who wanted to be able to be a Dragon. Obviously just casting the 8th level spell would be enough for combats, but I realized that you could put the spell into a Staff (called "Staff of the Dragon", cost 96,000 GP, one ability: Form of the Dragon III for 1 charge). That way she could burn 3rd level spells (or 3 levels of spell slots) and cast Form of the Dragon III, using her very high Charisma score for the save DCs.
It was then that I realized that you could break the game by making a Staff with Wish in it. "Staff of the Gods", cost 274,480 GP, one ability: Wish for 5 charges. Since staves don't require material components, this lets her burn off 15 levels of spells for a free Wish. Without bonus spells this would give her Wish 18 times per day. Plenty to give everyone +5 Inherent bonuses to all their ability scores (normally 825,000 GP), along with the general 'niceness' of being able to cast wish without cost. This could potentially be applied to other costly spells, such as True Resurrection (using Use Magic Device), somewhat breaking the game.
Is there something I missed? Do 20th level sorcerers really have the ability to break all game balance?
Any class can break the game if certain feats/abilities/etc are paired together. As a DM one of the most important things I learned was that just because the players can legally do it that does not mean I should allow it. At higher levels I give more leeway, but how much depends on the power level the group is using to gaming at.
It also helps to actually read the limitations on the base item itself. Staves can only hold 10 charges. Recharging a charge takes a spell slot equal to the highest level spell in it, and can be done once per day.It's not an issue of charges on the staff. The Sorcerer ability lets you expend spell levels in place of using charges. Effectively giving you 90 extra charges to be spread across items.
I think that this might be more of the issue of putting wish on a charged item. It is a powerful spell, and if you put it on a item to be cast a lot, there are going to be significant effects in your game.Normally this isn't a huge problem with wish, it can be used to make powerful/broken items (the Staff of the Gods is actually a fairly good example), but they're usually highly limited because each charge consumes material components. Wish 2/day, with a recharge of 5 days, is pretty powerful, but manageable at 20th level. The problem comes with the replacement charges that Arcane Apotheosis gives you.
I can see where that could be a problem. The fix I would use (won't eliminate the problem, but would curtail it some) is in the wording for creating staves. It talks about components, then adds in a way to make it cheaper...I'd simply remove the divsor. So any staff that has spells with expensive materials will always be needing enough material components to cast the spell 50 times.
*Edit:
Either that or put a limit on how many charges any one spell could require.
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I wouldn't be worried about an item like this if one of my PCs came up with the idea. It should actually make it easier to run a challenging game for characters of that level, as it ensures encounters.
Think of it: an item that powerful will attract attention. Gods of magic, law and order, and chaos would be interested in acquiring the staff. Evil gods and beings would covet it for it's power. Inevitables would be concerned for the ability to abuse the natural order of things. Ifrit could be jealous of such an item intruding upon their wish-granting niche. Many would want to possess it, many would want to destroy it, and some would possibly want to punish the individual who would dare inflict such an item upon the multiverse.
Plus, it's only good until a disjunction spell hits it. :D
Quick and dirty fix: You must use at least as many spell levels as the level of the spell to avoid spending a charge. That way a ninth level spell takes a minimum of 9 spell levels (and a very expensive staff) to use chargeless. The example wish staff would use 45 spell levels (5 charges * 9th level spell) to fire off a wish for free.
If you want to make it even stricter, add the following: If you choose to expend spell slots in this way, each spell slot may not be lower than one half (round down) the level of the highest-level spell contained in the charged item.
In other words, if you want to cast a wish using one less charge than normal, the cheapest way to do it is with one 4th level and one 5th level spell slot (or three 4th level slots, if you're partial to your 5ths).
Also, is the gp cost for the Staff of the Gods correct? According to the SRD, Epic magic items are those whose base cost is 200 000gp or more, which would make this staff an Epic Staff (and cost 1 million gp more), wouldn't it?
I didn't see anything in the pathfinder core book stating a limit on what a magic item cost...so...his math seems right. With them removing xp as a cost to make items or cast spells, and adding in a cash cost, it seems to reason that using cost to determine when something becomes an epic item is a bad one.
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Quick and dirty fix: You must use at least as many spell levels as the level of the spell to avoid spending a charge. That way a ninth level spell takes a minimum of 9 spell levels (and a very expensive staff) to use chargeless. The example wish staff would use 45 spell levels (5 charges * 9th level spell) to fire off a wish for free.
That seems a fairly good idea to balance out the "bang for the buck".
20th level is really hard to balance.
It was a LOT easier to balance before all of Pathfinder's hastily worded (and thus shoddily balanced) "capstones", which grant huge chunks of power with the wave of a hand.
I'm really not a fan of any of them.
Normally this isn't a huge problem with wish, it can be used to make powerful/broken items (the Staff of the Gods is actually a fairly good example), but they're usually highly limited because each charge consumes material components. Wish 2/day, with a recharge of 5 days, is pretty powerful, but manageable at 20th level. The problem comes with the replacement charges that Arcane Apotheosis gives you.
But staves currently can currently be recharged at no cost. Even without the sorcerer's special ability, a caster would still be getting several free wishes.
Using your example, one could buy or create three of your "Staff of the Gods" for 823440 gp and, over a period of time, grant a +5 Inherent bonus to all ability scores of everyone as well at no additional cost.
To me, this is again, more of an issue with the staff (and an issue with making your own magic items completely "by the rule") rather than the sorcerer even if the capstone should be reworded.