No. The US did invoke the Defense Production Act for certain medical equipment, to further ensure that its vaccine contracts are fulfilled first (<https://www.bloomberg.com/news/articles/2021-03-24/biden-use...>). (But, let me quote for others' benefit (<https://www.ft.com/content/82fa8fb4-a867-4005-b6c2-a79969139...>): "The DPA does not allow the administration to block exports overseas".)
The US's contracts would have been fulfilled first regardless (albeit more slowly) without the DPA, because (as I said) the US was the first and paid the most. We know this because the US's Pfizer contract explicitly prohibited the company from exporting US-produced vaccine doses until March 31, but the company only began to export US-produced doses at the end of April because it still had to fulfill said US contract first (<https://www.barrons.com/articles/pfizer-to-export-u-s-made-v...>).
Not how I understood it. But it seems you're right, the US only used war time powers to force companies to fill their orders first. The effect is quiet similar, the EU (not even UK) employed such powers.
In either case, it was argued that this made negotiations easier for US.
And yes, it's a fair point that it didn't matter, because the US would have bought the vaccines at whatever price point :)
> Except Italy as I mentioned, blocking export of vaccine to Australia that the latter had paid for.
Fair point :)
> ... and because the aforementioned collective effort was delayed relative to the US and UK
The UK (and probably the US) invested in supporting research, but EU closed contracts for vaccine purchases sooner. (I suspect the EU also sponsored research, but didn't attach strings the same way the UK did)
-----
To be clear, I don't think I would argue that the EU did fantastically well here. Nor that it couldn't have done much better. Namely because it doesn't have a powerful administration, like the US does. (I'm not arguing that it should have one)
Whether or not all this was unfair is hard to tell. Lots of countries poured money into R&D. (Also not sure how relevant it is).
But it is a bit funny that the EU largely let the free market forces play out, while the US didn't.