On the flip side, almost every cavalry soldier in an organized army in history has at least had some sort of sword or something to use in case it was needed. I'd say this would work better with the "Social Knights" or Cavaliers, as they wielded the popular Sword/Lance combo.
But when I honestly think about it, I think it could work out alright actually. I mean, take a Macedonian Hoplite (I always feel weird calling the soldier a phalangite, and calling them a phalanx just doesn't jive with me, so even though it's somewhat inaccurate, I hope you can excuse my naming), and a Hetairoi. The Sarissa was a much longer spear generally than the Xyston, yet the Hoplite managed to use it fairly effectively in combat. Sure the style of use was somewhat different, but in the end, they both fought in a fairly similar fashion (ie. move at the enemy until they are skewered). So yeah, I think it probably could work.