Imagine this scenario:

You are in the Underdark. Black walls of carved out rock make up
this tunnel that you find yourself in.

A dark-elf patroller is here.
A dark-elf patroller notices you!

A dark-elf patroller shouts "Zutra su er-dkra!"
A dark-elf patroller hurries towards you!

---

When this happens the mob will reach the player at the end of the
current tick, which is hard to predict precisely when but it could be in a matter
of seconds. If the player has moved out of the room at the end of the tick the mob will persue the player running, which means, if the player has moved 5 or less rooms away from the mob at the end of the following tick
he will be in a fight. In other words, the persuing mob can move 5 paces a tick and the player has to move more paces or the mob till catch up with him.

The shout could possibly be heard by other mobs of the same type who will come looking for the disturber.

This scenario is more exciting that entering a room and BANG you are in a fight.

It could be developed so that a camoflaged or hidden character could remain unseen and possibly a skill or spell to quiet or mute the mob without sounding an alert. Locations that are heavily guarded and dangerous to get into to could be much fun and rewarding to explore.
But if something goes wrong you better run like hell!

Any thoughts?

But existing ones were not designed with this in mind, and a number of them would be broken by it.

In your underdark example this could be used to lure mobs out of the way without ever fighting them.

In Aran gird, there wouldn't be safe spots.