Did Bethesda just forget about this basic thing during development or something? It's kinda hilarious. Someone wants to kill you and they're way too strong? Just leave the building or go indoors. They can't follow you.

I think it's not that Bethesda forgot; it's that they didn't think of implementing it, or that it was worth implementing. (Or at least that's how I perceive this, even though NPCs could open doors in Arena and Daggerfall.)

Also, I believe it's not strictly true; if you raise an NPC's Speed high enough (for example, by using what's commonly known as the Soul Trap glitch), the NPC should be able to go so fast that the game's collision detection fails to detect the NPC's collision with the door, and the NPC ends up on the other side. (This can easily happen to the player, and it's easier to see this, especially since you can also use the Super Potion trick (or simply use the console to cheat) to get your Speed high enough to break collision detection.) Note that, if the door leads to another cell, bypassing the collision will result in the actor going out of bounds (if you've played Daggerfall, you've experienced this, but Morrowind will send you back in bounds if you fall a certain distance).

By the way, in Arena and Daggerfall, while enemies can open doors, I am pretty sure they can't follow you between cells (so you're safe if you go inside (or outside) a house, for example).

Don't know why they didn't let NPC's walk through doors. Like dtgreene said, it is implemented in Arena and Daggerfall, and also in Oblivion. Limitations of the technical engine?
Whether or not you use this design weakness to your advantage is up to you (there are others, which are worse in my mind, like using doorposts for protection, if I remember correctly - was that in Morrowind or Daggerfall?). Morrowind (the base game) is not really a difficult game (unless you make it harder by introducing personal rules), and not using the "NPC door bug" is not going to make the game significantly more difficult.
Another example: In Morrowind you can fly (just like, say, the cliff racers :-)), but not in Oblivion. At the time it was explained with, surprise, limitations of the technical engine - in Morrowind entering or leaving towns is a seamless process (from the players perspective), in Oblivion it isn't.

Let's clarify: npcs can't go through loading doors but they can go through doors in the same cell. Many times I've seen skeletons come through closed doors to join the fight.