What you described with the health potions restoring 10% later still doesn't break even when it comes to the damage that these cave monsters deal every turn (not to mention stronger foes later). So I'm using a turn to heal, then losing more health than I gained. It's an objectively net-loss way to use my action.
You're right about using them out of battle, though.
Compare the Heal magic spell, which heals a good chunk of HP, more than the damage I receive during one turn. I've been using that, but when I face 3+ foes, I run out of MP before the fight's over and then I get killed.
I bought the first three badges, I don't have the 5 required to buy any more because I can't win these cave encounters and I'm too low-level for the black cat.
What do you mean by auto-defeated? I'm not sure what that mechanic is, I haven't been exposed to it.
Finally, if your suggestion is to go back to the first level and grind, that is a good sign that your game needs rebalancing, as a rule of thumb. Ideally, a player should be at a decent level to face whatever they come across so long as they clear out every screen they go through (you know, they don't actively go around enemy encounters).