Chain routing is possible in WH2, it's just not common.
You will see Shogun/M2 style chain routing if you are fighting Brettonian peasants (L36) or clan rats (L45). Are you ever going to get a similar result against High Elf spearmen (L70)? No way. The flat maluses from non-health sources of leadership damage are not going to make elf infantry rout. Most units in WH2 have pretty high leadership apart from some factions. Generals and heroes also have leadership boosting auras that push those numbers even higher. Most leadership penalties not related to the health malus are static: things like the "stronger enemies nearby" malus, "attacked in the rear" malus, fatigue malus, and so on. In campaign, then you add veterancy (scaling leadership bonus), technology (fixed bonus), lord skills (fixed bonus), and other miscellaneous factors like lord/hero followers, landmarks, world events, and other things.
Here is a reddit compilation of the leadership modifiers:
https://www.reddit.com/r/totalwar/comments/7q9p2y/compiling_leadership_modifiers/
This is the more accurate and complete compilation, but is less readable because it just has the variables from the game files:
https://twwstats.com/kv/morale?right=1678833570709893302
The scaling health damage leadership penalties are listed under total_casualties_peanalty which is what it stabilizes at. There's also recent_casualties_peanalty which is right after the unit takes damage.
Because of this, even a unit of High Elf spearmen (L70) is unlikely to rout until dead if near a general. If outside the general, it can be:
Half-dead: -16
Attacked in the rear: -16
Exhausted: -6
Losing Significantly in Combat: -8
Both Flanks Exposed: -6
Stronger Enemies Nearby: -8? I think?
Total: -60
All these together would make it close to routing: a half-dead tier 1 unit. To properly rout it you would need to do more damage or kill the general. Now, obviously, you can do this a lot more easily to swordsmen (L60) or to the aforementioned clan rats. However the leadership values are just so high that you're just unlikely to be able to get routs going before the units are near dead. Shock routs are just unlikely against many factions unless you do tons of damage on impact. When you have a battlefield full of higher tier units all with more L90, routs are just not going to happen even when the unit has lots of damage on it. One way to address this might be to just change the health modifier to be proportional. This would make it so that on an L90 unit, when it was 50% damaged, instead of it being a bitch-ass -16 penalty, it'd be a -45 penalty, which would be a whole lot more significant.
The other thing that makes it less common is something indirect related to how the pathfinding works. Charging causes a lot of leadership damage. It is hard to cycle charge units that aren't single entities in WH2 because the pathfinding forces units that are close to one another into combat. Overriding this automation requires that you spam move orders because there is no "Force Move" hotkey like in some other games. Your infantry or cavalry unit will keep playing melee combat animations and override your move orders which makes it harder to do lots of cycle charges. The slower and lower mass the unit, the more spam clicks you have to do to override the automation. This greatly weakens a lot of units that would be far stronger, especially because Charge Bonus is actually quite a lot stronger for multi model units than it is for most single entities.
The difficulty of forcing routs also messes with the balance of cavalry/chariots, because one of the strengths of that unit type is that you always get your maximum charge bonus against a routing target.