If I had to balance using health, just in theory I'd probably do it based on some kind of matrix based on footsie tools/walk speed, preferred range, and maybe potential damage output.
A character who is rush down/up close fighter but has poor walk speed and an extra large hurt box and depends on landing one BIG hitting combo, and has poor "get in" tools probably makes sense having more health. Treating health as a resource, they'll like need to "spend" more health to try and get in. Think a big body grappler in Street Fighter.
On the other hand, a character with solid walk speed, or good neutral/footsies, or high mobility should in theory have an easier time getting in, so they probably don't need a health buff, and if they have that Big Damage, then it makes more sense to treat them as more of a glass cannon. Kind of like a spellcaster in D&D style games.
It's obviously more complicated and subjective than that, and I'm not saying NRS is correct with their assessments, just saying that you could probably come up with a theory or reasonable explanation for why some characters have more base health than others.
The Kameos I'm not sure, other than just to make it a feature of the Kameo. Maybe you give up more pressure/combo potential with Jax, but he gives your character that extra health as a trade off.