We see it time and time again and it can be as exhilarating as a good fight. So, where are they? Currently, movement appears mostly tied to stats and latency. Following and shadowing. This is okay, for the most part, for your mundane movement around the world, but not for tense chases.
I propose a new skill: freerunning. Now, there's a clear issue with increasing the speed of movement, even at the high cost of stamina. Some people cannot react as quickly and that can ruin their enjoyment, it can aggravate people with higher latency, it can make the world feel smaller when you sprint across the sector at Olympic speeds.
Instead, a command (such as 'run' or 'sprint') wouldn't increase your speed but work as a sister to hide. When a person runs (perhaps it'd autotrigger on a flee attempt) they break into a sprint. They attempt to worm their way through crowds of people, hop over objects, maybe even knock some stuff down. The point is, however: they'd, at most, move a *bit* faster mechanically than normal movement.
The benefit: it'd hide you. Similar to hiding, higher freerunning and associated stats makes noticing 'their trail' easier as you're keeping pace, with a massive penalty placed on someone that isn't running. As you move with the run command on, your stamina drains heavily. Furthermore, perhaps if your freerunning rolls are lower but not horribly so, you might not be able to see the person in that room, but might get a hint at their 'trail of destruction' in a direction. At this point, you've realistically lost them, but might at least have some data on the direction they fled in. Like with 'go' run should be able to queue movement and idling for too long should kick you out of 'run' and inflict a massive penalty. ICly, this could be fluffed as you knocking into someone, crashing into boxes, etcetera, a similar something could occur on a bad roll when moving rooms while freerunning.
As this should obviously assist with your ability to flee, I also think it'd allow non-combat characters to still flourish in that they'll better be able to escape. Your assailant might be foregoing freerunning, so despite you being weaker, escape is a better option.