I'm not given enough detail about your specific game to know if this is relevant or not, but an interesting thought is that typically in RPG's, the enemies you fight take longer to kill as the game progresses, despite your damage output increasing. Whether or not this is just a way to add another level of difficulty progression is not really relevant, but the point is that if this is the case with your game, I can see HP bars with no numbers being a problem.
I say this because the first enemies you fight might typically take 1-3 hits to kill in a standard RPG, while late-game can see that balloon up to 5-10 easy. With only an HP bar to look at, it's going to give the impression that your characters are actually getting weaker, when that is not the case. Showing numbers helps mitigate this, because you have a reference for your strength. Doing 100 damage to a guy with 1000 HP would take ten hits, while doing 10 damage to a guy with 20 HP would only take two, yet with the damage popups, the player can still understand that they are 10x as strong, despite taking 5x as long to down the first guy. Character progression is a big deal to a lot of RPG players, and while there are other aspects to it besides damage (fancy skills, badass-looking weapons and armor, etc.) it is still a big part of the whole package.
Something to think about.