Health represents physical damage.
In real life there are numerous examples where feelings manifest themselves as physical effects. And mental diseases inflicting physical capabilities. In the anime there are examples aswell: Kakashi was for instance hospitalized after an encounter with Itachi in which he was under the influence of his genjutsu Tsukyiomi.
"Just because this is a genjutsu, doesn't mean the pain isn't real" -Itachi
Should be noted that with jutsus like Tsukyomi the caster is 1. very sustainable to counters from third parties as he has to maintain eye-contact, high levels of concentration, and has to remain still for the entire duration (could have to do with latter point), 2. You go blind and suffer extreme immediate drawbacks if broken / countered, 3. Has the intial condition of eye contact.
I expect the result of something like Tsukyomi to be like the effect of a Malzahar ultimate from League of Legends. E.g, tons of damage, easily interupted, large resource cost, channeled / damage according to how long it is sustained, fixed upper limit. With the addition of: Self-damage (severe if broken). Would be very effective in a 1v1.
How Malzahar ulti looks like (not important, look at the notes above instead):
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