The problem with this method you suggest is the coin is more than just an address it is an actual data object.
So you would need to create data objects for each split. Also once splits are occurring to the scale of bitcoin then the number of data objects stored on the network would be extremely large. So then you would have to be charging for these objects or someone could fill the storage of the network with one coin being split billions of times.
Even if you limited the number of splits of any coin and stored in the coin’s MD who owns what part (MDs are of limited size so number of splits is limited) then someone could overload the groups processing transfers with a very small number of coins. So the attack surface is large for this method too. Also becomes a problem if a coins is split the limit of times then the transaction has to be the size of the split that you own. Very awkward for trying to send small amounts because you may only have wrong sized amounts.
Have a read through the #safecoin category and look back through a number of suggestions for division. There are a number of them