Dark Souls 1, 2, and 3 are almost exactly what you described.
The combat is very much like you described, and although HP is a thing, it doesn't have the disconnected, number-grindy feel of an MMO. Imagine Skyrim-meets-LoZ with the combat diversity of Street Fighter. The differences:
Multiplayer: You didn't mention this specifically for your idea, I don't think, but this game is not an MMO... not quite. The way multi-player works is this:
This game is built as if it were a single-player game, and the focus is on PvE... very challenging PvE. The game is run on your system, not a server. You are, however, connected to a server that exists to establish P2P connections between certain players. If two players are in the same physical area of the game, and are within a certain range of character progression, they can be connected to one another at random. (The server rotates your connections with other eligible players very frequently, almost every 30 seconds or so.) Being connected to another player does not mean that you are both in the same instance of the area; your instances are separate. However, there are items that you can use to enter someone else's instance of the game.
1.) Place a "summon sign" on the ground via a re-usable soapstone. Players that you are connected to can see the sign in their world, and can choose to summon you by activating the sign. A white soapstone allows you to be summoned for co-op, and a red one allow you to be summoned for combat against the "host" that summoned you to their instance.
2.) Use a Red Eye Orb to force yourself into the world of a random player (called "invading"), with the supposed goal of killing the "host" to collect their "embers" (explained below) and some quantity of souls. You can, of course, choose simply to dick around and never attack the host.
3.) Join a particular covenant (imagine a hard-coded "guild" that functions as a match-making/lore mechanic rather than a tool for socialization or trading) that allows members to protect other hosts. If a host in another specific covenant is invaded, you automatically "counter-invade" to protect the host.
Perma-Death: There is no "perma-death" in Dark Souls, but every time you die, there is a consequence.
When you die, you respawn at a "bonfire," functionally a check-point and a hub for inventory management. Every enemy respawns as well, except for bosses.
The unspent souls (more below) you carry on your person are always at risk. If you die, you will drop your souls at the location of death. If you can get to them without dying again, those dropped souls are back in your possession. If you die before picking them up, they are gone.
Death also causes you to lose some amount of maximum HP. This maximum HP can be restored by consuming an item, called an Ember (in DS3). The restoration lasts until you die again. However, being "embered" will make you vulnerable to invasions from other players seeking to take the ember for themselves. Simultaneously, you cannot utilize a summon sign to summon help if you are not embered.
Character Progression: The progression has verticality to it, but you don't have to worry much about leveling up. You will only ever connect to people that are [X] levels away from you, and surviving any fight boils down to dodging, parrying, or blocking, but mostly dodging.
As you kill things, you collect their souls. You can use souls at a central location in the game to increase various attributes, such as Strength, Dexterity, Vigor, Faith, Intelligence, Attunement, and so on. It does not take long to hit the point of highly diminishing returns in a given attribute, so you don't need to invest a shit-load of time into a character to make them PvP-viable. If two people with roughly equal skill were to face eachother, one with a well-focused character at level 120, and the other with a maxed-out character at level 838, the fight would be on surprisingly equal footing. When match-making is restricted to others within a much smaller range of levels, no-one remains under-leveled for long.
tl;dr: Check out Dark Soul's game design.