Anyway, I've been shopping around and noticed that maximum current output doesn't seem to be a standard spec for batteries which seems odd to me.
I think you are mistaken about this. Any battery capable of providing current to drive a motor or other power-consuming device will specific it's current capability. Perhaps not in an obvious form. All those C ratings for Lipo and LiFepo batteries are a current rating. 20C which is typical, means that the battery can supply all of its available current in three minutes.