For a very fast battle format, where most standard fights last within about 30 seconds and boss fights somewhere between 2 and 5 minutes, I can see forgoing popups and just using the bar. Those games typically incorporate a fast moving ATB, and generally don't require much strategy, since the player doesn't have time to think about their attacks to decide the order of skills to use. These are typically good for games where spamming the attack button is okay, and quickly getting a magic/skill attack can provide an extra buff. Generally, the amount of damage is pretty significant, and you see the HP rolling downwards fairly fast, that popups are practically useless since they're immediately erased by the next bout of attacks.
I've played a couple of games like this.
However, for slower turn-based rpgs that are absent of an ATB and generally require you to strategize your moves, popups serve a better purpose, since they help you identify which attack has the most damage output, rather than relying solely on a slow moving HP bar, where it's hard to decide how much of the HP bar was removed from one attack to another, to determine your best moves.