I feel like you are misrepresenting Type B.
I can't think of RPGs that have low enemy damage while ONLY having low healing options. Starting healing spells may be weak, but later healing spells are always stronger and there are almost always powerful spells and items for emergencies. The trade-off, at least if the game is balanced or not just easy, is in the costs.
I mention Dragon Quest a lot as it is the quintessential JRPG and most RPG Maker editions are heavily based on it. In this case, Dragon Quest is a good look at Type B combat systems that I grew up with and which I prefer to base my games around. While a Type A game will have big swings of damage as the source of excitement and tension, a Type B game like Dragon Quest uses the dungeon as a whole to cause a slower, creeping tension. Picture this:
You enter the dungeon at full health, ready to clear the entire dungeon in one go. You get into a combat encounter pretty quickly and completely stomp, taking only 1 or 2 hits that barely did anything. You think this'll be easy and even downright boring. You press on and fight more and more enemies. Now you've taken a bit of damage but nothing serious. But your healing spell is only single target and everyone has taken some damage. So you heal the Mage (who took the most damage of course) and press on. No need to waste the MP to heal the Hero and Warrior that have good armor just yet. Going forward you fight some new enemies that still don't really hurt but have a lot of HP. Luckily a couple spells and they're toast. You keep going and find more of those tougher enemies, but now they teamed up with enemies that just smack you with status effects. After a few fights you have to heal everyone up. Now your Priest is at half MP and your Mage is starting to run low. After a few more fights you decide to save your Priests MP to cure the status effects and use items to heal HP. You keep on going but now you're running low on MP and items. Everyone's HP is okay but now any damage you take is going to stick. You fight more waves of cannon fodder monsters and watch your HP dwindle each fight. You wonder if you are too far in to just run away or if you should just use the last of your MP to use an escape spell. You reflect on how cocky you were in the beginning, thinking that a couple of easy mob encounters meant anything. Either you run away now or the dungeon claims yet another victim.
The goal of each combat encounter is NOT to actually kill you. The goal of the monsters is to throw themselves at you to make you waste resources on them. It is the dungeon's goal to kill you and the monsters are only there to force you into its battle of attrition.
In an RPG that follows the Type A style, each combat encounter is a test of skill with both damage and healing plentiful. Each battle is its own entity that creates tension through challenge - often with big bursts of damage that suddenly puts your HP in or near the red. Since healing is often cheap and easily accessible, as long as you can survive the battle you are generally fine for the next.
In an RPG that follows the Type B style, each combat encounter is a test of strategy and resource management with both damage an healing rather low. Each battle is just a cog is the greater machine that is the dungeon - each battle is not challenging on its own but contributes to the growing tension as your resources bleed out. Since healing is gated by spells (with MP a very limited resource) or items (which you can only hold a limited number of) each battle makes you steadily weaker for the battles after.
Dragon Quest in particular does this through its mob encounter design, which uses a few monster archetypes to facilitate its goal:
Weak enemies that appear in large numbers: These monsters use a numbers advantage to get in a few hits before they die.
Low damage, high defense enemies: These monsters want to either stall out the fight and get in a few hits while you whittle them down, or force you to use valuable MP on spells to kill them quickly.
Tank and Healer combinations: These monsters combine their strengths just like your party with a powerful, high defense attacker and a squishy healer to force you to focus the healer while the attack gets hits in or else the healer drags out the fight even if you team up on the attacker.
Reinforcement mobs: These monsters are not very strong but they can call in more of themselves in you do not finish the fight quickly. Some of these types also have high defense to force you to burn MP on AoE magic or else face a huge wave of high defense enemies.
Aggro Tanks: Some monsters are glass cannons that cast powerful status buffs on themselves to force you to focus them while their friends get in a free round of damage, or else you take a huge burst of damage after the turn delay.
Mage Party: Some monsters can use attack magic and they have an annoying tendency to to show up in groups so at least one of them can blast the whole party before they die.
Status Effect Town: Many monsters can use some kind of debuff or status effect, and unlike a lot of RPGs these are actually very good. Monsters that can poison your team up to try and spread their status effect before they die, monsters that use Surround become near-impossible to hit blink tanks if you don't focus them, some monster attacks have a chance of paralysis to prevent you from fighting back, and lots of monsters buff their team's stats and debuff yours. And they like to combine and team up.
That One Comp: Almost every area has an unusually powerful monster/comp that is higher level than the rest of the area and appears randomly. These are often monsters that appear in later, higher level areas and are just slumming it to mess up your day.
With the combination of insidious enemy compositions, powerful and draining status effects, and limited MP and items, a typical dungeon can easily take multiple attempts to clear. Especially if you want to spend extra time in them going for all of the loot. And since you can only save back in town, the entire trip to the dungeon and every fight inside of it are designed to wear you down. And at the end of it all is a tough boss fight that you will almost never be in perfect shape. Even if you grind and reach the boss with full HP and MP, you'll find that the boss fights are just like a Type A fight with tons of high damage and AoE attacks that require all of your buffs, debuffs, and healing to survive.
It also needs to make sure it doesn't fall into the trap of becoming a rhythm of attack > heal > attack > heal every turn, because that's not fun either.
