For multi channel audio discs, yes, the center has the same low bass requirements as the other front speakers. For movies, in practice, very low frequencies are kept out of the center speaker because the mixing engineers need to keep the channel open for dialogue, which is the most important element in a film's mix (from a mixing standpoint). Low bass eats up the available headroom in a channel, which is the main reason for the LFE.

Stereo subs operating with the left and right fronts (with center and surround bass re-directed) is a reasonable compromise given the nature of most source material.