From the now taken down Operation Warp Speed page, see here
https://web.archive.org/web/20210119000857/https://www.hhs.g... 300 million doses from AZ, 100 million from Novavax, as mentioned in my other comment 100 million from Pfizer, 100 million from Sanofi/GSK which as mentioned failed, and a 100 million from Johnson and Johnson.
Also mentions we signed the second 100 million dose contract with Moderna December 11th, that would be based their results which led to their submitting their application for an FDA Emergency Use Authorization on November 30th. See also lots of details on supply chain spending, well over a billion dollars.
So while you're technically correct, with how much effort it takes to ramp up production, see how Johnson and Johnson isn't going to meet their early 12 million dose promise, I don't see our general approach as being wrong. Signing multiple 700 million dose contracts would not in any way speed production, that only happens when you get an initial contract and start making it. Which is exactly what Moderna and Pfizer did, quite some time before getting EUAs, lots of doses were shipped within days. Where I live, for Pfizer the Monday after the FDA's Friday issuance of an EUA. To a hospital which had rented an ultra-cold freezer to store it, a lot of work and money has gone into this hole process.