The patents are the tip of the iceberg really. Most of the core technologies were developed with public funding. Oxford and Biontech got grant support for basic research. Some of the key rights are actually with the US government NIH who developed technology to allow the Spike proteins to be mimicked in a stable form.
What the pandemic has demonstrated is that there's a lack of manufacturing capacity globally. The US government was able to protect the supply chains for Pfizer and Moderna using things like export controls and the Defence procurement Act. Even so, firms like J&J and Novavax were left scrambling for US capacity and blocked from sending materials abroad.
I suspect, whether the patents are waived or not, the Biden administration expect the real money is in the process of technology transfer and licensing. Novavax have deals with Korea, India, Australia, Japan, Canada etc to make their product. But they still haven't hit production volume in the US, UK or the EU plants - so they're months away from being useful. J&J, a much bigger company, aren't ramping up fast either.
Moderna are effectively novices in mass production, but they got there and could now start doing the tech transfer for their product - and I bet they'll be handsomely rewarded for it. They've already said they won't try and enforce their IP rights on covid vaccines (as have J&J). My money's on the US government deciding exactly which friendly nations deserve such tech support.
Pfizer clearly know a lot now about both the vaccine and the manufacturing ramp-up and have started to share that with their pals. If they get encouraged (ie: paid now and in the future) to share it more widely as an instrument of US foreign policy, then they will. The fact that they may be able save millions of people won't be lost on them either - the people who work in "big pharma" aren't generally monsters even though it may look like that at times.