Warhawk Riders with Spears should have longbows as well, shouldn't they? That's how they were on the tabletop :)

Ideally, yes, you are correct, however, since CA has focused in these games on having units identified by one weapon only, such as knights continuing to fight in protracted melee with lances, which is somewhat non-sensical, and the fact that the riders do not actually use their weapon in close combat, I focused on representing the unit as a melee only variant with a high charge bonus, to fill a different role than the archer version, rather than just replacing it with a better version, which would stop people from recruiting the vanilla version.