No, it wasn't like this in IGAU. I think this is a great balance thing when done right but Supergirl and Catwoman taking less damage than some characters is actually super weird for example lol
Even when done right 'great' is stronger praise/credit than I'm willing to attribute to variable health values. At best, to me, it adds a bit of flavor by allowing certain characters/character archetypes to be tank-ier than others. In most cases though it's just a lazy half-assed nod towards balance.
IMO the hierarchy of what determines a characters strength goes:
Tools > Mobility > Damage > Stun (if applicable AND variable) > Health (if variable)
Giving a character shit tools but a metric fuck-ton of health = shit character
Giving a character OP tools but the tissue paper durability = Upper Mid-tier or better
Hell, frequently the extra health thing doesn't even work out well due to other design considerations. For example in Blazblue: Calamity Trigger the character Iron Tager has ~8% more health than the next highest character in the game and ~27% more health than the lowest health character in the game and he suuuuuuuuuuuuuuuuuuucks. The funniest part is that because he's so big most of the other characters get Tager specific combos that significantly break the ceiling on their normal damage output rendering the extra health pointless.