I was struggling with this conundrum, open to thoughts of others. My tentative conclusion is BTS does not earn income at all, at least in the traditional sense.
If a company earns income in USD, its underlying asset base rises due to the profit. It can then:
1) distribute this profit to share owners as cash (dividend)
2) use the cash to buy back and burn shares (effectively distributing cash while increasing the value of remaining shares) or
3) keep it retained in the business to increase the value per share.
In each case, there is a return to investors in aggregate as a result of the profit. Importantly its the profit that drives the return, not the form of distribution or re-allocation.
Without a profit, representing an accrual of value of assets held by the entity, no change to the share structure (e.g. burning shares) adds value to the group of owners as a whole. Therefore burning per se (a mere change in ownership structure after the fact of value-creation) cannot be considered income of the entity, and it does not lend any increase in valuation to the entity as a whole.
As BTS (and derivative bitAsset) transactions occur, and BTS are burned, the value per share rises, but the value of the entity does not. There has been no externally-derived value to the group as a whole that can be distributed. There has only been a transfer of value from those burning BTS through transactions to those not. Doesn't this mean that the BTS burning through transaction fees, which we often designate as "income", does not give any value to BTS at all?
This line of thinking has led me to wonder if any crypto-asset can theoretically earn profit, in the traditional sense of the word, unless shares in it represent ownership accrual in things that exist outside its own share ledger. For example, a company has a balance sheet made up of assets outside of its own shares. I think the only way this can be replicated in our ecosystem, or to create "profitable" DACs, is with a resource management system built around the required block-chain(s), that allows the use and improvement of other assets in order accrue more of them (an example is that Music is forced to manage assets (like music tracks) outside the Notes block-chain).
If there is no income, value accretion is driven solely by the increasing utility of the coin itself in use or exchange. This is also potentially a valid approach, but is not so different in approach to most other crypto-currencies in general.