I mean sure, you can just look at your own numbers and say "well when I use this class/loadout I'm averaging about 34k per hit but this other set-up is doing 60k, but it's also a bit slower" and form there you're stuck just estimating which one overall will be the more effective/efficient approach. Thing is people simply learn things differently (not "better" or "worse," just different) so while "crunching the numbers" is fine for some, others do better being able to "eyeball it" with a visible gauge.
That's also assuming you can even read the numbers coming off the enemy in the first place. If I'm playing one of the older classes with a consistent, relatively slow paced combo loop, then sure I can compare my numbers to the same class, and maybe even a different one if I put some effort into it. Scion classes? Good luck with that. I can catch that a hit has a different amount of digits at best. Part of that's also due to power creep though.
But yeah HP bars (or similar features like HP-gated breaks) are nice, especially when stuff gets fast-paced. Good to future proof stuff if they build it into the system in a good-looking/feeling way early. Like you said, non-intrusive and preferably immersive. Doesn't even have to be a bar, just some way to measure progress with granularity. We kind of already have that, but those usually come with phase changes so it's kinda useless when your effective DPS output changes with the enemy patterns. Plus you get the opportunity to remove the bar to escalate.