One theory would be that anything that makes the plant more relaxed and comfortable overall frees up energy for reproduction. You see this in many organisms.
That's funny because some other plants produce seed better when stressed. a rootbound fig tree is a great example of this. It's like the plant is saying okay I don't have much time here left on this earth so I need to reproduce.
I found with daylilies the earlier you can get out and do your crosses the better. If I wait until after lunch to do my crosses the chances of setting a pod are not as good as say 9am -10am which for me seems to be the sweet spot. If you get out there too early there won't be many pollen grains on your anthers and if you get out there too late the grains are no longer as fluffy. That's just from what I've noticed since I started crossing daylilies. Of course that's only been since spring of this year but I've gotten many pods to set this way and missed a few pods from doing my crosses too late.
Another thing I found is fresh pollen works a lot better than pollen that is stored even if it's only stored for less than 24hrs, the fresh pollen seems to always do better for me. I know many hybridizers swear by it and don't get me wrong I have gotten a few pods with pollen that was in the fridge overnight but I got way less pods that way vs using the pollen fresh. I know your selection is more limited on a day to day breeding program but whatever works best seems to be the route I usually take.
As far as seed count goes I've noticed most of my tet pods had on average 7-10 seeds per pod a few only had 1 or 2 seeds per pod and I had one with 16 seeds in 1 pod but most hovered around the 7-10 mark. Some of the plants with the highest seed count for me have been Forbidden Fantasy, and Forestlake Ragamuffin. Both are very fertile both ways and make up the majority of the genes in my crosses this year. As a matter of fact the seed pod with 16 seeds was Forbidden Fantasy X Forestlake Ragamuffin.
It's great when fertility notes are added to the database, this will give you a great idea on what to expect out of your daylilies when hybridizing, although with most daylilies this info isn't mentioned. I can tell you that Forestlake Ragamuffin has some Super Pollen it's what I got a pod on a dip with and almost every cross I made with it took, It also sets pods very well. Forbidden Fantasy pod setting capabilities are out of this world and it has good pollen also. Others talk highly about Dragonfly Dawn being highly fertile both ways much like Forestlake Ragamuffin and so it too will be added to my breeding program next year.
Here are a few others I have used and my thoughts on them. Grams Dream has decent pollen but doesn't set pods well and I'd go as far to say it's no good at setting pods. Kabuki Drama is fertile both ways but it's pollen is slightly better than it's pod setting capability. I would not rank it up there with Forbidden Fantasy, and Forestlake Ragamuffin as far as fertility. Collaboration sets good pods but it's pollen isn't the best in the world either. Double Cupcake is not a breeders daylily I haven't gotten a pod on it yet and it's one of the few dips I grow. Francis of Assisi is the same way, I got pods but they aborted and no pods where set with it's pollen. Jo Barbre is another one of the few dips I grow and is fertile both ways but isn't the one of the best breeding daylily out either. Avante Garde will set pods but not easily also it's pollen isn't the best in the world. Restless Heart will set pods but I can't say how fertile the pollen is because I haven't used it as a pollen parent. In my garden the trend seems to be the more fertile the parent plants are the more seeds per pod but this is just an observation in my garden from just 1 year of hybridizing.
As far as your question of can setting too many pods cause less blooms the next year I can say this much, all my plants are 1 year or less and I set or attempted to set pods on every flower that formed. I haven't gotten any increases from my daylilies that had pods this year and I suspect this is the reason. my single and double fans plants are all still single or double fan plants with the exception of Green Arrow, Double Cupcake, and Francis of Assisi which didn't have pods or whose pods aborted. So I'd be tempted to say it does indeed take strength away from the plant. Maybe clumps wouldn't have been affected as much but I think I pushed my plants as far as they could go for 1 year old plants and will be heading into 2017 with the same number of fans I had spring 2016 because of it unless they'll send up more fans come spring.
I look at every flower as a chance for a new daylily and even though I haven't noticed any increases I'll have a bunch of seedlings next year because of me pushing them as hard as I did. All my new plants next year will be pushed the same way. I've heard way too many stories of people loosing new dayliles so my new theory is " use them before you loose them"