These are two diametric opposites in how you want to express
challenge through combat in your game. Do you want the challenge to be about finding ways to win each individual encounters ("acute" challenge as I like to call it), or do you want it to be about minimizing resource expenditure through the course of a dungeon ("chronic" challenge)? You can have both types in the same game, for sure, but at the very least as a designer you should consider that they are very different types of challenge that should be kept somewhat apart from each other if they appear in the same game.
Most of
@bgillisp's concerns about full heals after every battle are completely valid - however, I think when this manifests it often speaks to bad battle design. Acute challenge tends to encourage full heals but full heals necessitate that there is a high
variability in the outcome of battles. You should be able to walk around the world map, get into two different battles, and reliably get two different results from using a similar strategy. Action battle systems are obviously a good way to do this. Tactics games like
Fire Emblem or other games where you only take part in a few battles per hour tend to fit this. Otherwise, there should be mechanics that force very situational tactics to be use and greatly reward or punish the player for adapting well.
Persona 3/4 did the "acute challenge" thing really well - the Knockdowns and "1 More" bonus attacks meant that when your party was of equal level with the enemies, you might finish a battle without taking a scratch or you might be Total Party Wiped depending on how well you exploit the enemies' weaknesses. These games do
not give you the full heal after each battle, but they could if they wanted to.
On the other end of the scale, "chronic" challenge works best when the player can make clear risk/reward decisions over long periods of time, the game has a heavy emphasis on time or resource management, and/or the game's dungeons/levels are designed to take a predictable amount of time/steps to run through. Roguelikes are perfect for this kind of thing; traditional RPGs can fit this well too as long as they wisely
limit the amount of resources that the player can bring with them (Mana, Healing Items, etc.) and
don't allow the player to get badly lost in dungeons (this completely kills the fun that can come from running dungeons in such a system). The key needs to be knowing what to use and what to hold back as the monsters whittle down your health - if the player can just heal themselves up after battle without thinking twice, you might as well skip the middleman and give the player a full heal after each battle. One other type of game that tends to take well to chronic challenge is the game where permanent progress is earned at an extremely slow rate -
BoF4 Dragon Quarter and
Azure Dreams are really good examples - the strength you earn over long periods of time allows your minimal resources to last longer so you can keep adventuring.
In practice, there is room for a middle ground between these extremes. Some games have genuine "chronic" challenge in dungeons but give you a full heal before the boss battle (this can be harder than you'd think to pull off correctly, though, because almost by necessity the player will have items, etc., that can give them a huge advantage in what is supposed to be an acute challenge in the boss battle). Some games give you a partial heal after battle (like most
Tales Of games), essentially whittling down your resources over time but allowing you to keep going if you play the battles perfectly. Some games give you the full heal after battle, but present extreme acute challenge in their battles, and introduce the chronic challenge by forcing you to use precious resources as trump cards to win a battle when things aren't going your way (this creates a spectrum of outcomes - easy win, win only by using resources, defeat, etc.).
The issue at hand here is that MP attrition (slowly depleting MP until it's gone) has a couple negative downsides. Firstly, when you get a new cool ability, you don't want to use it, because it's likely more expensive and you need to save all your MP for an inevitable lengthy boss fight. Secondly, it's just not fun to run out of mana, or even have to click dozens of items to recover. Thirdly, you're often presented with the choice of using mana for healing or for damage, when there is a clear correct choice to save it for healing.
This is certainly a problem that a lot of games with small MP pools face. In my opinion, designers need to be more creative about designing battle mechanics around MP use and about keeping HP and MP mostly separated/differentiated so that most situations don't allow you to convert one to the other (either directly, like in a healing spell, or indirectly, like in an obvious choice between a Health Potion and Mana Potion).
In a couple of my games, characters have Mana and Adrenaline. These are both used to cast the exact same set of skills - you can choose to cast a skill from either MP or AP. However, Adrenaline starts fairly low at the beginning of each battle and regenerates each turn, whereas Mana carries over from battle to battle and can only be restored by resting at an Inn or using precious items. Thus, you can have fun with skills in every battle without worrying about conserving your Adrenaline, whereas if you run up against something really tough you can use your Mana to cast your most powerful skills more often.