Sure, in a single battle you want to route the enemy as fast as possible.

But my point was, that in the next battle all those troops that ran away are fully restored, so yes the winning tactic is to have light cavalery to chase them down, (which is what they were used for in real life, too.)

So Sun Tzus advice to sometimes let the enemy run away on purpose, so their fear infects other enemy troops for easier future battles - is not captured.

Yes, that's correct; it's not captured. In TW, I believe it's always advantageous to run routing troops down. In real life, not necessarily.

If people learned from what happened to others that running a way isn’t a good idea, wouldn’t they get more motivated not to do that?

Is that not modeled in that game, or is the effect so small that it doesn’t make a large enough difference?

In some TW games this is slightly modeled in, in the sense, that a unit might choose to fight till death, rather than running away, when they are surrounded and they have nowhere to run. So then you open up a way .. and they will try to run again, which is easier to finish them without own casualties.

But those are hardcoded algorithms.

The units do not really learn. (that would be awesome, but is very very hard to implement in realtime in a proper way) They just improve their stats with experience. So they get stronger in stats in either case, even when fleeing every single battle.

At least for Rome Total War and Medieval II, experience does mean a difference. A veteran army will fight for several times longer against overwhelming odds than a newly recruited one before breaking. It also depends on training: even green Roman troops will last longer in prolonged battle than green Gallic ones. Do not remember how later games deal with that. One thing the author of this series stresses is that battle is very emotional and you can't learn from a book that running away is a bad idea.