Best illustrated by example.
Say you have 2 12V batteries in series that are 100% charged and giving 24V
If you drain both batteries to 80% charge and then recharge them, they are both at 100% again. No problems there.
If you drain one battery to 80% using a 12 volt feed the other one is still at 100%. This means you can either put up with one battery lower than the other, or try and bring it up - but as the same amount of juice is flowing through both, you are trying to make one battery 100% and the other one 120%! This results in much boiling, hydrogen and general distress on the part of the overcharged battery.
It would work if you were taking out a small amount and recharging the batteries independently on 12V chargers at regular intervals, and/or only taking a small amount out of one of them but I don't think it would work well in the long term. From what I can gather on here the boys that run 24V challenge winches mostly have 2 batteries for the 24V system and a third one for the 12V system running off two separate alternators, as you described.