what are the benefits or drawbacks to changing the hatch day: July 1, October 1, and January 1
If you ask ten people, you will get ten opinions. Some of that will have a lot to do what breed they have, and where they live. When the birds are hatched will have no impact on their genetic potential. My April date was only an illustration on how important point of lay is to the qty. of eggs laid in the pullet year.
Always make comparisons within a given hatch, and you will do no harm. Birds to grow at different rates in different seasons, but genetics rule at the end of the day.
Some breeds would be important to hatch early for some. I could see where a breeder of Brahmas would want to hatch early, even with your Jan 1st date. I would recommend discussing this with a breeder of Brahmas. One that has done well with them. For many the hatch date has a lot to do when the birds would be in their prime during show season.
One of the considerations, and possibly the largest consideration, is the growing environment. You are always looking to achieve good steady growth, without repeated growth checks. An example of something that can cause this is extreme weather changes. I try to achieve a large percentage of my birds growth before we get especially hot. I try to "beat the heat".
Another consideration could be timing a fall hatch where they will be coming into lay as the days are getting longer in the spring vs. coming into lay when the days are getting shorter. Cull pullets are also easier to get rid of in the spring than they are any time of year. Especially that they are not "spent" hens. There is a lot of people that want to get birds in the spring that do not want to hassle with raising chicks.
I had preferred to hatch my birds in early March. My Catalanas want me to do other wise. If I hatch too early, they are prone to molting during their first winter. They mature sexually especially fast. I think by hatching April 1 this year will not be too early or late. They would be laying well before show season. It could be that hatching them later would be better to hatch later for the shows, but I like my pullets laying by 6 wks before my hens molt.
I prefer the flowing with the natural rhythms of the seasons vs. struggling against it. I have grown into enjoying the seasons and the particular things that naturally flow within the seasons.
We do all find our own rhythm, for our own reasons.