The problem with the system is that it's hard to say what the difference will actually be, rather even between just the ice age characters in my one settlement the base health range is 109 - 173.
The real issue (and, so as to not panic the devs, it's not much of one) I find is that because you don't get very many of each age the odds of you getting a "good" example of that age, one that plays to it's strength, can be pretty small.
as to not using low health characters, I'm not sure the devs are really trying to encourage you to do so, the system is sort of a play what you want thing, I for example use pre-industrial\time of magic characters a fair bit (one of my characters has a base health of about 45) because I like the extra damage (said character has been upgraded to about 212% attack power). but I also have use Skelebots for when I just need gobs of health, and Ice Age characters for when i want to take the tension off (being good allrounders)