More sensibly, if we want the FDA to make delivering a particular set of documents a sizable piece of its job, we should (through Congress) direct that and allocate appropriate funding for that purpose.
From a Reuters article on it: They also argue that Title 21, subchapter F of the FDA’s own regulations stipulates that the agency “is to make ‘immediately available’ all documents underlying licensure of a vaccine."
So it really sounds like this is just part of the course of making sausage of approval. You have someone already embedded in the licensure project/process where this is all (very likely largely automagically) handled as it is always expected to be released to the public.
A lot of cash was dumped into fast and extensive R&D, trials and production scaling because of the urgency of the situation, and along comes an insane documentation backlog.
To put in perspective, the original HPV vaccine R&D and trial spanned over 7 years with 25,000 patients (of which only 20,000 women), and assuming the documentation was provided to the FDA as it was produced, it could be FOIA'd relatively quickly.
Pfizer/BioNTech did the same, with almost double the patients, in just over 6 months.
Damned if you do, damned if you don't.