While I think simplifying the health types is great idea, I think this might be too far of a swing in the pendulum.
Maybe on top of health/armor/shield you have something like humanoid/robotic/infested added in? (not really sure where to throw in sentients, fragments and a few others atm)
I feel the thing that confuses new players and aggravates the older ones the most is when, for example, you have heavy gunners and bombards: both are grineer, both are humanoid, but each one uses a different armor type. And you can't tell which is which in the middle of a mission, only with prior knowledge.
So maybe cutting down on a few health types and setting a few ground rules to stick by would make things more intuitive without over simplifying things? Like all humanoids, across all factions, use ferrite armor and anything robotic would use alloy armor.