The speed thing is more complicated that I remembered. A thread specifically about it:

https://forums.totalwar.org/vb/showt...=cavalry+speed

It's quite possible that my tests with Scouts failed because Scouts have no stamina bonus and simply become tired before they can catch an enemy General. War Clerics are in the same boat I think, but Huscarls (IIRC) do have some stamina and should have the same mount as Mailed Knights and I still don't remember ever catching an enemy General with them. I'll have to check it again.

I didn't address offensive sieges either, where I'd usually avoid bringing swordstaves just because they're not killers even if you use NA to force the enemy out of the square.