You can't "hide" the blockchain form the state without simultaneously hiding it from everyone else as well - i.e. the majority of the population who don't hold private keys and on who'm you're depending to endorse its value.
Anyway, this whole idea of treating blockchain "cash" as if it's a credit paradigm - where bookkeeping for an individual's state of credit doubles up as 'money' and therefore needs to be hidden from view is slightly ludicrous.
The obvious solution is to de-couple the problem of fungibility from the priorities of transparency (as every other cash medium since the dawn of man has done) and create a fully transparent AND fungible blockchain. That objective is achieved by showing the outputs but mitigating the build up of regular patterns in the blockchain such that one balance is practically indistinguishable from another in all respects other than address.