No one does the same damage, no one has the same mobility, everyone doesn't build the same meter per combo, not every person on the cast have a dp, no one weighs the same, everyone is a different height, so why does everyone share the same health?
Okay, I'll list stuff that makes me not like health as a balance mechanic:
#1: It completely deletes 'universality'.
There are always char specific combos yes, but you can still choose universal combo paths that will do the same thing to every character.
With different healthbars, the very same combo may work on every character, but you still sometimes need 2, sometimes 3, sometimes 4 touches - depending on who you do it on. This is obscenely confusing in about all aspects ("This combo deals 33% life, except against Chars B and C where it does 44%") - you're used to it due to FG experience etc, but believe me, it *is* confusing.
To put it into a perspective you're not so used to looking at: Imagine every character had an invisible Mana Modifier which determined how much meter the opponent actually builds. So eg Modifier .9 means that a move which would usually build 100 Meter only builds 90. Now your very same combo which works the very same on differing characters sometimes builds 0.5, sometimes 0.8, and sometimes 2 bars - depending on who you do it on. This sounds pretty fucking confusing to me.
#2: HEALTH IS NOT A TOOL.
You can't use Health in the neutral for anything other than "I'll be allowed to do more stupid stuff". Mobility is a tool that you use. Metergain is not directly a tool, but gives you earlier access to Supers/DHCs/makes you a better Battery/etc = Tool. A DP is a Tool. You can't use health.
Character height and weight are stupid and I hate them to hell and back, that doesn't make Health better :^) At the very least, Height and Weight add something to the game in terms of versatility - differing combo paths open up, mixups change, approach angles need to be adjusted, etc. Health doesn't add anything for anyone.
#3: Extension to #2: Since it's not a tool, it doesn't actually solve any problems.
If you have a shitty Grappler and increase its health by 500%, it will still be a shitty Grappler. It will be S-Tier now, but it won't be fun to play either way - it hasn't gained anything other than switching risk/reward in your favour so you're allowed to run more bad guesses. The only way for health balancing to actually make a character feel good is if it had all the necessary tools to compete to begin with, but shitty risk/reward on them due to dying too fast. Which implies that they had too low life to begin with (= Were not a standard 1000 Health character, but a 850 HP one).
IF you really think that the tools of your character are sufficient and the risk/reward is just not good enough, increasing Damage Numbers work the exact same as increasing Health, except it doesn't run into the Issue #1 and still requires you to land a hit to get a benefit, rather than allowing you to get hit more often (= Plain better)
#4: It will affect all matchups (almost) equally.
This is not a problem for designing your game from the get-go with differing healthbars in mind, but one HECK of a problem for ever changing life.
Normal balance looks like this: Parasoul has a problem with Peacock? Buff Bike, which is one of her main Anti-Peacock tools that's not used much elseways. Peacock has a problem handling fast rushdown characters? Improve c.LK's hitbox, which won't really come into play in the v.Painwheel matchup, but shuts down IAD approaches. Cerebella has a problem with projectiles? Improve Reflect, so.. etc
Health balance looks like this: Cerebella has a 3-7 matchup against Peacock and a 5-5 matchup against Painwheel? Buff her health by 15% to make the Peacock matchup about even! Oh shit, the Painwheel matchup is 8-2 now. Uuuh.. improve Painwheel's life too, I guess?
#5: It is fucking easy to keep the same.
Ideally, every character would have the same overall mobility, the same tools against everything, the same health, the same damage. Now, that'll happen if you have a roster of one character. As soon as you add characters, and try to add versatility, you have to go down the "Give him more of this, take some of that" path. One char will lose a bit of mobility and gain a projectile to fight at long range. Another character will lose the DP special move and gain better hitboxes on its normals to keep the opponent away.
How do you keep damage the same when people have varying tools which they hit with at differing times? Even if you kept all frame data and damage on all normals universal, one guy would deal more damage due to hitting for 1000 damage in Fireballs at a range where the opponent can't do anything, and another will get bonus damage from being able to combo out of his unique special move, and whatnot. Damage will always fluctuate, there's no way around it. Health.. doesn't. So why force it to?
Changing Tools adds Versatility. Changing Tools has the 'issue' of also changing Damage between characters, which you try to balance out. The only thing that doesn't fluctuate at all and is in perfect balance at no cost of versatility is Health; why the crap would you want to rip that apart?
And then there's the visual aspect of two same looking healthbars (eg both exactly at 50%) actually representing different numbers, the everlasting problem on whether you should go by %age or net health to determine which character is in the lead (Eg Char A has 1000HP total and is at 50% - 500; CharB has 2000HP total and is at 40% - 800, which char is in the lifelead?), the aspect of player feelings on the damage vs health debate (Fighting a high damage character = Being on edge, scared as fuck of getting hit ;; Fighting a high life character = Being bored to death, getting frustrated that nothing moves the life bar), and probably more I'm forgetting.
E: I'll not talk about Guts because that's a completely busted mechanic only there to add 'hype'. What a fucking shit.