Card benefits are convex in the costs. Just take a look at the basic Treasure and Victory cards. And in the case of action cards it is the same. A deck with 5 2$ cards is certainy worse than a deck with 2 5$ cards.
A deck with 5 Fool's Golds is better than a deck with 2 Outposts.
Making King a 9$ card would be nonsensical as it would rarely be bought instead of Platinum. It is pretty difficult to reach a Colony with one or two Kings whereas it is much easier with one or two Platinums.
And in a Province game you rarely wanna buy an action card instead of Province unless it is early in the game. If you had ever played a game with Prince you would be aware of this.
King would be bought at $9. If Herbalist can be bought at $11, King can certainly be bought at $9. You are underestimating the value of +Buy and coin tokens.
It can definitely be worthwhile to buy an action card over a Province in the mid-game, depending on the deck-type. Mega-turn strategies don't green until the very last turn, and many strong engines will not green until late.
About the proper worth of GM without the copper restriction, it is probably slightly above 7 as Donald priced it at 7 without the extra buy during development. It surely isn't 8.
GM is easily worth $8 and is often bought with $8 in hand. Seriously. The $7 buyless version you are talking about is not relevant because it's from an early version in development and Donald made no comment about its balance at that time. A later version had +Buy and no Copper clause at $7. It didn't stay that way.
Your claim that a +1 card, +1 action, +1 VP token, +1 coin token, is worth 8 shows that you have not really thought about the issue.
Your hypothetical 8$ card is just a Baker with +1 VP token. The latter hardly justifies a price increase of 3 given that Monument has a price increase of 2 (assuming that a hypothetical terminal silver is worth 2, Duchess is the benchmark for this claim).
Yes the hypothetical card is Baker with a VP token. I did think about that. I think it's a good starting point because a cantrip VP token card is powerful and dangerous. The price increase of Monument over Duchess has no bearing here. Those are terminals and these are cantrips. Your comparison shows that you don't understand how cards are priced. Smithy is $2 increase over Moat for just +1 card more, but Lab is $3 up over Great Hall.
Maybe this hypothetical card really would be too weak for $8. If so, add back in one thing or the other, or put it at $7. Or start testing there. King with all the bonuses is almost certainly too strong for $8, and Grand Market is the proof.
An average King will most likely lead to fewer VPs than an average Goon or Bishop.
If so, it would be because you can get Goons/Bishop earlier and they can accumulate more VP in a single play (Goons with multiple buys and stacking, Bishop by trashing high cost cards). So what? Those are terminals, King is not.