Mounted crossbowmen (and harquebusier/pistolier) were invaluable for the sedentary army that lacked a horse archery tradition to have a modicum of mounted missile firepower - they were no substitute for the real deal though.
Lance already enjoyed a sort-of prestigious position among the Europeans, so I am not surprised that they found the lance skill of Poles and Cossacks to be most valuable - even if they had a much more diversed skill set.
Plus, for ambush and raid you would prefer to ride close and chop/impale the victim (likely defenseless peasants etc) anyway.
Not saying it was easy, just that:
a) IMO it is about as hard as parrying most other weapons.
b) it was likely actually attempted in the past.
c) I'd say parrying longsword with a dagger is actually HARDER than parrying a couched lance with a short spear.
Someone mentioned Paulus Hector Mair a few replies back, and I go dug around wiktenauer for his treatise - apparently he taught parrying couched lance with another lance, although not in a way I envisioned it (the parrying knight actually grip his lance with two hand).
That will be the case if both knight and horse archer are moving in the same direction, i.e. if the knight is chasing after the tail of horse archer, then his sprinter-type horse may well have the acceleration advantage to catch up with the Mongol (disregarding encumbrance difference etc)
More often than not however, when the knight was moving toward the Mongol, the Mongol would move out of the way to the knight's left hand side (since that's how he could aim his bow most conveniently), forcing the knight to change direction, so no "sprinting" happened in the first place.