I respectfully disagree. In May and June - when I most generally get a broody, the bugs are really coming out and going strong. The broody in July, is because (I think) we had too many dark days, and the birds did not get enough light.
I think that light has a huge influence. I noticed that people would start celebrating or complaining about getting broody hens much earlier in the spring than I ever had, so I started asking if they added light, and those that replied, said that yes, they did. Most of the people on here provide most of their chickens feed with a commercial feed, so I do not think that their intake of food quality falters that much, and thereby causing broodiness, which I am understanding as your view.
Generally speaking with animal husbandry, one gets better reproduction with good feed. Although I have read studies where people have brought in cattle and dry lotted (without feed, but with water) them for two or three days, then put them back on pasture and then added the bulls. They claimed a much higher and tighter conception rate, but it is not a practice that is either practical for us or interesting. We get very good conception rates by meeting our cattle's needs, pulling the bulls out and culling open cattle. I do realize that one cannot transpose studies across species, but I think it is the breaking of the fast with good nutrition that stimulates the reproductive track, not the lack of nutrition.
In poultry, if a bird is laying consistently, I consider her major needs are being met. If the worm load gets too high, or the quality of feed drops, or she just is not getting enough, the bird will stop laying eggs. A non-laying hen is not going to go broody, even though a broody becomes a non-laying hen, when her clutch is established to suit her. A well fed bird, who has her nutritional needs met, will put on weight, so that she can survive the setting for three weeks.
I think it has to do with the amount of light, or length of day.