Ultraviolet light is well known to be damaging,
https://www.nedcc.org/free-resources/preservation-leaflets/2... ("Protection from Light Damage")
https://www.loc.gov/preservation/care/light.html ("Limiting Light Damage")
[late edit]: And if you search the literature, gamma irradiation is known to affect the texture of certain fruits—and if you ask why, one of the studied mechanisms is that fruits' cellulose polymers—which paper is also made of!—are easily broken by gamma rays:
https://sci-hub.se/https://doi.org/10.1002/pol.1957.12026114... ("Effect of gamma-radiation on cellulose" (1957))
> "Cellulose is degraded at gamma-radiation dosages equal to or below those required for softening plant tissues such as apples, carrots, and beets. Therefore it seems probable that the degradation of this cell wall constituent is a major factor in the radiation-induced softening of plant tissues."
The effect on thin, old paper should presumably be the worst, no?
[edit]: And this paper says the lethal gamma dose for one species (different one) of pestilential beetle is 1,000 gray, or 100 krad. That's a bit higher than the threshold doses for cellulose damage, from the other paper: 34–64 krad. Stressing that I have no clue know how those numbers translate to paper integrity.
https://www.nature.com/articles/s41598-023-43739-x ("The lethal and sterile doses of gamma radiation on the museums pest, varied carpet beetle, Anthrenus verbasci (Coleoptera: Dermestidae))
So it comes down to picking the dose that doesn't kill your but does kills what would other wise kill you... radiation cancer therapy.
The only obvious advantage of irradiating them would be that it will kill eggs; if the eggs will still hatch in an oxygen-free environment, there's no advantage and plenty of downside.
Anyway, I wouldn't suggest irradiating them either. Just the volume of required handling would ruin them.
You could have an environment that was consistently oxygen-free, but it would make no sense for eggs laid in such an environment to refuse to hatch there.