How to create a machine is intellectual property.
Are we supposed to believe the global capacity to create a certain machine is somehow maxed out because Pfizer is trying its hardest? What part of it cannot be achieved faster?
Not really. Pfizer would be taking responsibility (or at least signing off on) the equipment/process/product etc. I wouldn't call that IP. It's also not a given that any drug manufacturer can simply outsource production of such specialized/sensitive stuff. Many/most other drug companies are simply not in the mRNA vaccine business, and the ones who are are developing their own vaccines.
I agree with you that if everyone was working together to get this done then it could be done more efficiently. But there are issues of ego/pride, money, credit, liability, and other precedents that would be set that preclude this.