Though personally, I think shifting strategies mid-game is more doable when HP bars are showing. Like I could play defensively when the HP is still huge, then as it drops, I begin using a more offensive strategy to finish it off. If I don't see the HP bar and there's no other way to determine how much HP is possibly left, then I'd probably stick to a single strategy for the whole fight, which is mostly, heal when necessary while continuing to attack.
You mentioned this earlier, but without or without HP bars, I think one can promote mid-game strategy shifting through creative enemy attack patterns. Personally, I think that strategies that come from knowing or not knowing enemy HP should play second fiddle to strategies that come from enemy attack patterns. I'm a big fan of boss battles where bosses have different "stances" (altering its weakness/resistances, what kind of skills it will use and on what targets, or even creating field effects, etc.), multiple parts with different roles/functions, or the ability to summon allies mid-battle, etc.
Also, even when there's not a visible HP bar, the player
does know that the remaining HP is dropping lower and lower. The player can watch closely how much damage they've dealt and take an "educated guess" (based on the difficulty of previous bosses, the difficulty of the most recent regular enemies, losses on the same boss battle, whether the boss seems like a more powerful foe than others) as to how much HP they
think the boss has left. This can create a tense psychological situation where, as the player is running low on MP or items, they might decide to risk an all-out attack in the hopes that it will be enough to take out the boss. These kinds of risks also involve degrees of confidence, where the player has to think, "Okay, if this maneuver fails to take out the boss, what is the likelihood I'll be able to able to regroup and still maybe pull off the win?" If they figure that the odds of survival should the assault fail are basically zero, they might decide to risk it, or they might decide to scale back the attack a little, saving some MP or turns that they would have used for damaging spells so that they could heal. It can get pretty dramatic, especially when the last save point was outside the dungeon. (I recently had this kind of experience while fighting Hein in Final Fantasy 3.)
Visible HP bars largely mitigates this kind of tension, but replaces it with the kind of decision-making that comes from knowing how much HP is left. Again, it all depends on the effect you're trying to achieve!