I'm gonna hazard a guess that the birds are not free range? If you quarantine the chooks from the outside word, then of course bird 'flu isn't gonna be an issue.
It's an interesting facet of the situation and worth looking at. Incidentally, it's a good reason to advocate for battery vs free range farming.
Within a single country, the risk of bird flu being introduced is about 2-6 times higher in a free range farm than a cage farm. I can't find solid data, but I'd bet that the cases where it's most different (closer to 6x higher the risk) would be countries like Australia where the outdoor situation is harder to control and they do a good job of quarantining the indoor cage farms (if you know anyone in Australia who works on such farms you'll know about how strict they are with people keeping pet birds, keeping clean before going into sheds and between sheds etc). While in third world/poor countries like where I'm based, just about everyone has chickens running around at home and even if they don't, like me, they have all the neighbour's chickens running around the streets, coming into their kitchen pecking for scraps, everyone shops at the local wet market where all sorts of animals dead and alive are on sale, running around, etc, and no one understands let alone bothers with quarantine efforts, yet these places remain absolutely 100% immune to supply or price issues. No one here even knows there is an issue, let alone cares let alone tries to do anything to stop it, and there is no problem, yet every single Western/White country in any corner of the globe is dramatically affected. Given the difference in quarantine effort etc, a cage farm in a backwater third world country should be at far higher risk than any farm in Australia, or even if you want to completely ignore different standards between countries, the problem here should be at least half or so as bad as Australia, but here there is no problem at all. According to the official story, bird flu is 90-100% fatal to the birds in a flock, it spreads very effectively in cage farms, and there is no effective quarantine between sheds here, and they're not doing mass culls, so the egg industry here 'should' have completely been wiped out by now.
If there was something of a trend, there was some amount of correlation on a spectrum, sure, I'd think battery vs cage is likely to be a big part of it, perhaps even the main issue, but it's very close to an all or nothing issue, even though cage vs battery methods themselves are on a spectrum, the highest profile case of egg shortages, the USA, primarily uses cage farming (and even their 'free range' eggs are mostly indoors but not in individual cages as opposed to running around outside). But the numbers don't seem to add up.
If your idea is correct, we could simply solve the entire problem immediately by switching back to cage eggs, which incidentally is not a night and day difference in animal welfare, it's an apples and oranges deal. Animal welfare lobby groups have to push for the less economic option because otherwise they can't justify their existence - you are redundant of you push for what industry wants to do anyway. If you've ever been to cage and free range egg farms you'll see that in terms of welfare they both have pros and cons. Given an apples and oranges welfare situation I'd go for the one which is most efficient - better for prices, better for the environment, and if it's safer from a disease perspective that's also better in all respects including animal welfare.
Edited to add a picture of the eggs I bought from the wet market yesterday. I went for chicken rather than the usual duck eggs because I haven't won the tipping contest recently and my budget didn't allow for duck :'( But weirdly, in plastic bags like this is how most people here buy their eggs, or in the cardboard crate things if they buy 30 or more at a time.
In Australia (15+ years ago) I used to think of eggs as a cheap form of food, and 10 years ago in Asia I didn't eat them too often because compared to other foods they were expensive - barely cheaper than Australian prices but other foods were dirt cheap. Some other foods here have about doubled since then (due largely to inflation) and eggs are now a more budget friendly option relative to alternatives.