Interesting video!
Question though: can't eggs last for months on end, even kept unrefrigerated? Do they not last long enough, unfrozen, to cover the periods of their not laying?
Lasting unrefrigerated depends on many factors
1) Where you are. For example the USA wash eggs before sale. This removes the bloom that seals the egg pores that renders the shell safe against bacteria. I wouldn't trust such an egg more than a day unrefrigerated.
2) Current room temperature. We have an egg surplus right now Yesterday it topped 40C here . Again, no, I wouldn't trust eggs stored in very warm weather for months.
3) How old the eggs are when you get them. Many shop bought eggs are weeks old at the point of purchase.
Certainly eggs can be stored at cool ambient temperature for several weeks if unwashed, from a clean nestbox etc. I've seen no studies on how long they remain safe but it might well be worth testing!