You can only do this if you delegate authority and trust, in other words, if you build hierarchies with power and enforced trust. The DNS system is a hierarchical system, where the top nodes have a lot of power ; but in a no-double-spend system, this power becomes financial. If you need a hierarchy of trust that you will get the correct information that Jack, who is trying to pay you, has NOT double-spent, how can you know that this hierarchy is not colluding to make you think that indeed, he didn't, while in fact he did ?
How can you be sure that one is not HIDING this former spending of his, the time that you accept the payment ?
How can you check that nobody is putting more coins in circulation than is officially announced ?
If you have to trust specific hierarchical entities to tell you about that, the decentralized and trustless system is out of the window.
The whole problem of a truly decentralized and trustless system, is that you are not to depend on ANYBODY to be able to check the validity of the payment one proposes you, and the amount of coins in circulation. It means that anyone, at any time, must be able to check this independently if he wants to. This is not possible if there is a hierarchical system in place, because in such a system, you are DEPENDING on these centralized authorities, that can tell you whatever they want.
Yes, you can think of a system with different hierarchies of COINS, where you have a master coin that is the reserve currency of master nodes, who each of them are in a constant exchange rate with sub-coins of a different nature which can themselves be the reserve currencies of still other nodes with sub-sub coins. However, if there are random payments from sub-sub-coin A of subcoin B, to owners of sub-sub-coin C of subcoin D, then, if you want this to be trustless and distributed, the users still need to have all these chains, to be able to check the right-to-spend of coin A, the right to exchange to coin B, the right to exchange to the master coin, the right to exchange of coin D and the right to exchange of coin C. Yes, you might think that you don't have to bother about subcoins F, H, J etc.... but even that is not true, because you want to check their quantities in circulation.
So in the end, if you want this to be trustless, this is just a different way of organizing the transactions, but in the end, you have to know all of them, if you want to check the total liquidity.
I have been trying these kinds of things for quite a while, and I'm coming to the conclusion that there is no real way to have a system that is truly decentralized and trustless, and at the same time, scales without having an increasing burden on the individual user, who has the choice between delegating more and more trust to central authorities, or having more and more technical costs.
Well, there IS such a system, which I'm favourable for, but I'm not sure it is stable: that is: many small *independent* currencies, with floating exchange rates, and connected through decentralized exchanges. But my fear is that speculative forces will put a hierarchy into these currencies, bringing us back to the current situation. Nevertheless, at least, that is a system where the burden per user doesn't increase with adoption: a user decides to use just a few small crypto currencies. If he needs to pay another user, he has to find a way through exchanges to get his coins, with several intermediaries, converted into the tokens of his counter party. That's clumsy, but at least, it scales, because the number of steps is logarithmic with the number of users.