I understood that poultry, like other species which develop from eggs are born with a finite number and when the limit of these approaches and hormones change, henopause occurs. The peppermint theory would have some positive implications for endangered species breeding programs if it reeely works
The effect, as I read it, is in relation to having commercial layers be more productive & therefore financially viable before their use-by date. It's not going to make the finite number of eggs change, just have them producing more & "better" eggs before their commercial lives are at an end.
I wouldn't specially feed something to my flock that may shorten their egg-laying lifespan (as you say, there's a finite number of eggs to be had... my understanding, like yours, is that this applies to any animal or bird with ovaries), but then I don't have a use-by date for my hens for that purpose. I would happily plant a peppermint plant & have them pick at it as they chose to, however... and do plan to have a herb garden especially for them to pick at as they wish (plan that's been in my head for more than 5 years now... one day !).
If I were breeding, particularly a rare chook breed, then producing as many good quality eggs whilst the hens are younger may be valuable. As you say, it may be valuable for endangered species breeding programs, too... if it works on species other than Gallus gallus domesticus.