I think you have an excellent point that, unlike many other Potion-cost cards, P.Stone has nothing unique to offer; it only gives Coins, which are always available in the form of Silver and Gold. But in the kind of deck that wants P.Stone, it surpasses Gold very rapidly. That's without using every spare buy on Coppers, even. It gets to $3 quite rapidly and should be worth from $6 to $8 before game's end.
Actually Pstone
doesn't rapidly surpass gold without a lot of aid. Take a simple game where you buy exactly one card a turn with no drawing (e.g. Scav/Pstone). On T5 Pstone is worth a Silver. on T10 Pstone is worth a gold. On T15 Pstone is finally worth $4 ... right when the game is about to end.
How about Familiar? Well let's say you dish one curse on T6/T7 and two on T8/9/10 and two/three on T11/12/13 and still gain a single card a turn. This means that
at most a Pstone has gold value on T13 of just $4. Yes that is better than gold, but that is a lot of busted hands ($2P), overlooks the fact that you may need to play Familiar (dropping card count in deck/discard) to get decent treasure density in hand, and that there are LOT more ways to build up gold in a Familiar deck (e.g. Taxman, Mine straightforwardly or something simple like Smithy), and that even at end game that Pot not being a Silver counts for a decent number of VP.
For any limited gain setup, Pstone only spends a few turns more valuable than gold; with the drag of an early Pot on building money density I'm doubtful that most anything will be able to watch Pstone surpass Gold by game end (barring stuff like I already have a Pot for Familiar).
Of course the actual +coin value is less important than its space efficiency. Consider something like Cache. It is worth 3 and comes with two coppers. Why is this such a weak $5, it has the same in card coin density as gold, but you have to deal with 2 other cards. Sometimes that isn't too hard (hey I've got some Apothecaries). Sometimes you don't care about space efficiency - you have a way to make the space inefficient cards work for you.
Scav is like this, you simply don't see 75% of your junk ever ... but Pstone is slow at beating Gold that it doesn't matter (particularly once you start top decking Scav instead of Silver or Gold). You need something that gains you more than a card a turn (and preferably more than 1.5 cards a turn) to really be competitive with Gold.
But once you have the ability to gain those masses of cards you run into another trouble. Oddly in Dominion, Pstone does not want you play the stuff you buy. Normally if you buy some junk you might want to sift past that crud, but if some of it gets into your hand (say with terminal draw) it doesn't really matter. So you can do things like Madman/Cache where Cache becomes a cheap Plat (hey I'm drawing 25 cards, coppers are bonus). Cache gives you a gold with 2 "junk" cards, Pstone normally needs at least 5 "junk" cards to hit Gold in the early game. If you draw your Cache "junk", it is just gravy (e.g. Madman/Cache makes for cheap "Plats"); if you draw your junk with Pstone you lost Pstone value.
Even just the cards it takes to sift can really slow down Pstone's value gain. Something good, like Warehouse, might be able to churn through 14 cards a turn ... but at the price of lagging a turn or two on the value of Pstone. Cellar engines can churn more ... but each card in play is dead to your Pstone. To beat gold, Pstone needs to have 25 cards in the deck or worse have 22 with Pstone and a single discarder. In order to chain most sifting you need a lot of sifters which normally decrease your buying power (e.g. Cellar or Warehouse) or you need some Sifting Engine. The latter can actually work ... but that is a lot of cards that support a lot of other options better.
If you are looking at game end by say T20, that just isn't a lot of turns with those $8 Pstones (as you know, you hit them on T20 if you gain 2 cards a turn on average).
Fv: Pretty poorly. The only time it is really useful is when you have something that can eliminate your Potion for your (e.g. Apprentice). Even if you have just Coppers/Colonies/Hparties/Pstone and +buy, you need a lot of coppers to make PStone useful (as all your Hparties will be in play reducing Pstone's value), further because you have so many coppers you have really low odds of drawing 2 or more Hparties in your starting hand or with a Hparty play.
Maybe it might work at some point, but you need a decent bit of support.