Technically speaking, bitcoins are not a complete mathematical abstraction, they do exist as entries in the blockchain. And I don't think that such a representation of money substantially differs from how fiat in its digital form is instantiated on the Central bank accounts. Just in case, fiat can be divided into smaller units too, though there is no reason for that due to inflation. More often, the reverse procedure is required, when bigger denominations are replaced with smaller ones. For example, 100 Benjamin Franklin dollar bills may get replaced with 1 Donald Trump dollar bills in the future...
Regarding how much better a real money can get, there is always a lot of room for improvement