Alive and laying eggs is a good start. Feeds that do not keep the chickens alive, or have them alive but not able to lay eggs, are not what you want either.
Laying eggs is a reasonable indicator of good health in laying hens. Missing nutrients will cause the rate of egg laying to go down. Hatchability of eggs will tell you a little more, because sometimes a hen can lay eggs but they don't have all the right nutrients to produce a healthy chick.
If you track down the research on individual nutrients, you can sometimes find how they set the recommended levels. For some nutrients, like salt or calcium, too little or too much can make the birds less healthy and less productive. There is an in-between amount that seems healthiest. For some other nutrients, there is a sliding scale where one amount is not enough, more is better, even more is better yet, and higher-yet levels are expensive enough that it's not worth the money commercially. Sometimes there is level that is so high it causes problems, other times you will never really get a high enough amount to cause problems.
I'm generalizing because I haven't studied it enough to know about most of the individual nutrients, just the basic ideas.
I'm not trying to say that the research gives the optimal level for chickens to live a long healthy life, but people who care about profit will care somewhat about the health of the chickens, because dead or unhealthy animals do not produce well enough to be profitable. So up to a certain point, their goals do overlap with yours. That makes their research one amount useful even for backyard flocks. The trick is to know where their information is correct for your purposes, and where it is not, and that gets complicated!
I'm glad to see that U_Stormcrow is going to post about it when he has time. He has studied much more than I have about the details of chicken nutrition.