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The only point I don't see you making that is important about paying free agents is that they generally tank more than they provide a pleasant surprise (that's my intuition at least).  Let me state it this way.  If you made a bar graph of the dollars spent per win for all free agents, you'd see an extremely assymetric distribution extending to positive infinity on one side (actually it is worse than that because you can pay money for worse than replacement performance) and zero on the other.  What is really desirable is to know the median $/WAR value and that is what you want to shoot for, not the mean $/WAR.
Regarding your general point, surely you can pay more than $4.5M/WAR and have it be a good idea even from a finances point of view.  Those playoff games make money and have a significant impact on attendance the following season.  Making the playoffs, versus missing them, can make a team tens of millions of dollars, so the player acquisition that converts you from an also ran to a World Series winner is worth a lot.