The 21 day thing is not a rule, it is a guideline, a target you should shoot for. Chickens are living animals. There are very few true rules where you have to do something one specific way or civilization as we know it will be forever changed. Practically every recommendation on this forum is a guideline or a target that you should aim for, not something rigid you have to meet. You have to be flexible in your approach.
There are a lot of different things that can effect when the egg actually hatches, humidity, heredity, how and how long the egg was stored before incubation started, and just basic differences in the eggs. Size is one possible difference, but thickness of the egg white or shell porosity are others. There are more, I just don’t know what they are. One really major difference is average incubating temperature. If the average incubating temperature is a little high, they can be quite early. My first couple of hatches I had eggs pipping when I went into lockdown so I adjusted the temperature down. If the temperature is low, they can be a few days late.
Even after I adjusted the incubator temperature so that most of my hatches are about on time, I still get a few that are a day or even two full days early. I’ve also had some hatches a full two days early under a broody hen though most are about on time.
As Egghead said, some people don’t get the day count right. There was even a hatching calendar on this forum that had it wrong. An egg does not have a full 24 hour day development two seconds or two hours after it is put in the incubator. It takes 24 hours for the egg to have a day’s worth of development. In theory, it takes 21 days of development for chicken eggs to hatch, so the day of the week you set them is the day of the week they should hatch. If you set them on Friday, they should hatch on Friday. But that is only theory. In reality, they can easily be off a few days either direction. I figure if they hatch within 24 hours of the target time they are right on time.
Most of my hatches are over with about 24 hours after the first one hatches, whether under a broody hen or in the incubator and whether early or on time. But some drag on for more than two full days, just due to some differences. Each different incubation is its own adventure. You don’t know how it will turn out until it is over.
The study you are talking about has already been done. You can find the results by going to the extension websites and reading the articles. Just look for the recommendations. The commercial chicken industry often partners with various universities to perform those studies. The chicken company provides funding and a grad student performs the studies and writes their thesis on the results. That’s where a lot of the recommendations come from. There is a major difference though. The commercial industry use incubators that can handle 60,000 to even 120,000 eggs at a time and use several of these so they may hatch more than 1,000,000 chicks a week. Where a one or two percent difference in hatch rate won’t mean much to us, even a small difference in hatch rate is really significant to them. Most of us are not going to notice if we are off these recommendations a bit. We’ll still get pretty good hatches. We will not notice a 1% difference in hatch rate, but if they are hatching 1,000,000 chicks a week, that’s over half a million chicks a year. And our goals are different. We can let hatches drag out for two or three days. With them, they want the hatch to get over so they can get the incubator back into action. Due to how much heredity affects when the chicks hatch, one of the recommendations is to not select your breeding chickens from the ones that hatch late. That is not important to me. Be flexible.
Hopefully this helps a bit. Good luck with the hatch.
I asked yesterday, but haven't any interest yet! 
