That's a very good analysis, and you touch on some of what bothers me about how we "value" WAR.
The price teams are willing to pay for expected WAR is an expense. To apply that retrospectively and label it as "value" leads to the logical conclusion that teams are underpaying all but the most awful performers. Which, in turn, makes it easy to justify destructive contracts. (IMO, of course.)
That doesn't mean it's not a good tool to put things in perspective. But, as you state, it's important to remember that what teams are really looking for isn't to spend $9m per win. It's to blend your spending so that you grudgingly pay one or two players at the $9m per win level, a few at the $85K per win level (like the Sox did with Devers last year) and the majority somewhere in the middle.
That's a long way of saying that from the team's perspective, the value of a win is a linear expression of what they expect from their total payroll, not what the top end of the market is expressing. And this is why all but a few free agent contracts end up being seen as overspending on the team's part.
I love Mookie, but I think a 12/420 contract for him would cripple the Sox and I want no part of it.
I think we basically agree.
Obviously, teams want to hold down their $/WAR. You don't want to pay retail if you can avoid it, for all kinds of reasons: keeping costs down and keeping flexibility up. But that doesn't mean that the observed market price of a win in FA isn't an important consideration in understanding how the different, intersecting markets for talent work and interact: the anti-competitive market for homegrown talent (a.k.a. the draft, draft-slotting, and arbitration system), the IFA market, the trade market, and the actual FA market.
You seem to be proposing that we instead use $/WAR of the
entire market as our benchmark, and I see why you might do that. This narrows the argument to thinking about to different ways of expressing the delta between the value of a pre-arb player and the value of a FA player. The Fangraphs way has us price players' projections in terms of the FA $/WAR, and then subtract their actual paycheck to determine a surplus value figure that you can compare to another player to determine relative trade values that roughly correspond with observed values. You seem to be proposing instead that we give each player both a projection and a $/WAR unit price, as it were, and use that to measure surplus value.
It's not a terrible idea. But the problem is that because that includes sections of the market that are — ahem — over-regulated, those prices don't actually contain a lot of information. So you end up blending the signal of your FA market in with a bunch of noise from the pre-arb tranche of the market, in which players of widely divergent quality all earn roughly the same salary. Rafael Devers makes the same money as Matt Chapman, who is probably a better player than he is — but both guys also make the same money as Joey Wendle, Rio Ruiz, David Bote, and Mike Freeman. No offense to those guys, but they aren't in that same tier.
I'm worried that you get a less-sensitive measure of the cost of a win. You also get a measure that requires a bit more math to make effective trade comparisons for different lengths of team control.