The fact is that the Aircorps would not pay Allison to develop a two speed or two stage supercharger for their engine. They were told to put a one speed, single stage supercharger on the engine and the GE turbo would do the rest. This is essentially how the installation in the B-17 worked as well.
Unlike the turbosupercharger, gear driven superchargers must be designed with the exact engine in mind - so it is the job of the engine manufacturer to design a good one for their motor. The best example is what Hooker did with the two stage unit on the late model Merlins. The ones that made the Spit IX and the P51D so fantastic at high altitudes.
P&W were just about the first to have a two stage geared supercharger on a high output engine - the Twin Wasp installation on the F4f. When it worked, it was just what the plane needed, but the supercharger was tempermental. P&W went on to put an effective 2 stage unit on the R2800, used in the F6f and F4u. But developing these units took many years and lots of money.
Allison can be criticized for a lot of things (for example, Doolittle complained how dirty their factories were early in the war), but it is not their fault for following the contractor's orders.
-Blogs
Originally posted by Captain Virgil Hilts
...There are any number of reasons that the Allisons were never equipped with a two speed crank driven supercharger, although none of them are particularly good reasons. Mostly the reasons given have to do with simplicity, expediency, expense, and related excuses. The Allison could have been equipped with a two speed supercharger, it just wasn't. ---.