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Because only the inventor can invent
Just take some items from another discussion to make the point - manacles.
You have poor manacles (level 0)
and higher ones going up in DC. The poor ones would be in your formula book - but you realize they aren't good enough and you want to craft average ones (level 3).
You are in Absalom - no problem - go to a shop, buy the formula and craft some. Or buy an average manacle and you reverse engineer it.
Now move your party to the Mwangi Jungle - 3 weeks away from any town. You find yourself in a tiny Hamlet with an old anvil - and a captured enemy that you want to secure - but all you have are the poor manacles.
The inventor invents a new formula and creates better ones.
So in principle that gives you access to common formulas anywhere. Depending on circumstances and where your adventure happens, this might be very valuable or utter useless. The reason I used Absalom vs Mwangi Jungle.
It still won't sidestep high rarity items as that would undermine the whole idea of access. It still is a rare formula - even if you have access.
The GM can always allow you access - and as GM I would be more inclined to relax this RP wise for an inventor as for someone else - I use the idea of if it makes sense/is plausible then I don't try to block a player - but as player you can't demand to have access to rare items just because you are an inventor.
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Common-only because rarity is meant to help the GM limit options which do not thematically fit a campaign/setting, are limited to certain groups/areas, or are simply difficult to find because there aren't many around. Something that would be worthless if it is undone by an easy to access feat.
Also - if you are the GM adding a homebrew item to the setting, then you can set the rarity as common if you wish. Which would make it a valid option for Inventor.
If you are a PC just trying to make up your own homebrew in the middle of a campaign, then you are completely reliant on GM permission, a feat absolutely should not be a way to try to get around that.
Common-only because rarity is meant to help the GM limit options which do not thematically fit a campaign/setting, are limited to certain groups/areas, or are simply difficult to find because there aren't many around. Something that would be worthless if it is undone by an easy to access feat.
Also - if you are the GM adding a homebrew item to the setting, then you can set the rarity as common if you wish. Which would make it a valid option for Inventor.
If you are a PC just trying to make up your own homebrew in the middle of a campaign, then you are completely reliant on GM permission, a feat absolutely should not be a way to try to get around that.
I agree with your general point, but there are plenty of feats which grant access to uncommon options. That said, they do it in very specific ways, where this would be throwing open the gates for anything.
The common formula bits also sidesteps the issue of players trying to make up their own items, which PF2 is not really built to handle.
As others have said, it's only common because that's all that the game by default says can even be purchased in the first place. If your GM is lenient with what you can find and purchase in a town, then they'll probably also be lenient with what you can invent with this feat.
Also, it's worth noting that many very powerful items are common. Common only refers to the rarity system, and can be anything from level 0 to 20.
Lastly, I don't even see how people making up their own items is relevant here. No matter how the feat was worded this wouldn't be allowed within the rules and would require GM approval. If there was a feat that allowed you to create something that's not in the rules, then there would need to be rules on how to create that item... but then it's in the rules, which is a contradiction. It's either an impossibility or you can just create anything you want for any made up cost and call it any level of item. Which would essentially make you a God.
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I agree with your general point, but there are plenty of feats which grant access to uncommon options. That said, they do it in very specific ways, where this would be throwing open the gates for anything.
Fair. I should have been more specific in differentiating between feats that grant access to specific uncommon option(s) (i.e. class feats giving an uncommon focus spell) vs the suggestion of a feat allowing open access to anything uncommon. The first is basically normal and expected in many areas of the system, while the second would break several purposes of the rarity system.