To me, these seem like marginal benefits. If knowing where your food comes from is important to you for some reason, by all means, carry on.

However, every scientific discussion I’ve ever seen on organic food has found the same thing - there is no significant difference in nutritional value between certified organic food and nonorganic food. Of course, “certified” organic food is still industrially produced - just according to arcane regulations that make it more expensive. You could make a case that “organic in spirit” food is more nutrient dense in some way or other - but the lack of a real scientific definition of “organic in spirit” will make it harder to study, and I have not heard any scientific discussion of this. And improved health in people who eat organic foods are corrolational, and can be chalked up to these people caring more about their health in general, and being wealthier. All the most robust science on diet and health points to the same thing - the big factor is simply avoiding junk food. Getting farm fresh eggs is just a way to show off how much money you can throw away if you use them to make french toast covered in locally tapped mapel syrup.

All that to say, I really doubt you would find any noticeable health difference.

The benefit of keeping chickens and eating their eggs is that you get to enjoy the process. You get to watch your chicks grow into chickens, feel pride when you get the first batch of eggs, and enjoy eating those eggs (which I find are tastier than the cheapest ones at the store that I buy - though I think the taste is comparable to the fancy high price eggs my friends sometimes feed me). Do it to enjoy the process. But don’t do it under the illusion that you are saving money, saving the world, or saving your health.