Or should he be invincible like in Wario Land II or 3?
Personally I'm torn on it. I liked the novelty of the 2nd and 3rd game, but I felt that it made many puzzles and boss fights more annoying than fun. You effectively died in one hit against just about any boss in Wario Land 3, since you got knocked out of the arena and forced to restart.
I can go either way, as long as his health isn't absurdly low.
Something like 5/8 health bars is the sweet spot.
They could even have a difficulty setting where picking the easier one takes away the health bar, makes you invincible like 2 and 3 and then you can get hit and screw up as much as you want.
I think it depends on how many transformations/reactions there are, I really love how they went all in for WL3 and having them everywhere is a lot of fun, and I feel like there's less of them when they coexist with a health system. So I'd love to see them make an invincible Wario again.
I love the concept of arena bosses and think they have a ton of creative potential, but in execution I think dieing in one hit is a bit too cruel. It's fun having the tension of getting hit but still having the chance to recover and I wish all of them were like that. I remember in that rabbit boss it's 3 hits and you're out which I like the idea, but when actually playing it that boss was kind of frustrating so I think they definitely can use a little polish.
Wario Land 4 and Shake It had some amazing bosses, and in particular I think WL4 did the health system the best because I feel like the enemies in Shake It aren't that aggressive with all the health challenges, and also in WL4 transformations can appear during bosses, but instead of knocking you out of the ring, they waste time which you need to win and also for the treasures
I'd say I'd rather have a health bar or else the game will be usually punishing in very unfun ways like giving you transformation which will waste your time which very annoying to say the least.
Personally I find that the reactions being annoying/time-wasting in II/3 is part of the intention, since they paint Wario as very stubborn and determined to get what he wants, even if it means repeatedly put himself through such humiliating effects. That said in 4's case the game is designed more around traditional platforming, and adding a health bar was definitely the right choice in that game compared to 1/VB's more traditional power-ups. Pizza Tower goes a step further by having the best of both worlds: you're immune during regular levels so you can focus on scoring, while the bosses give you health to make them more traditionally challenging.
If we were adding a health bar to a potential Wario Land, I would say maybe tone it back a touch from what 4 did. 8 hits is a lot and makes the entire normal mode a cakewalk, but even in hard and super hard mode I find most levels are easy if you can snag a couple of hearts, not to mention the hidden power-ups that top it off.