the axle acts as a spacer between the two bearings, preventing excess side loads to the bearing races... if that "spacer" shoulder isn't long enough, then the axle will see the brunt of the damage, and the slop will become worse
some axles in sealed bearings use a separate sleeve over the axle. Others employ a two shoulder axle design.
either design, i'd install a thin washer or two to take up the excess end play... then reassemble, being mindful to not apply force that will crush the sleeve or shoulder on the axle.
the bearings should seat up to the hub completely as they also contact the axle sleeve or shoulders.