One thing that could be done is to add a new rule to the minimum fee structure that adds a relative increase in the minimum fee after a year or so, in such a way that long term savings accounts end up paying for their past security eventually; but that's not really demurrage and doesn't contribute much to consolidation of the blockchain nor does in contribute anything to the running security.
There are no rules to the minimum fee structure - miners and nodes are free to enforce whatever fees they want. Ultimately the market will decide what fee structure is best for Bitcoin, which is the way it should be.