Not going to take personal offense at your question like some others do but:
... a distributed ledger system ...
But what if we had a system that works with decent security that doesn't rely on that cryptotoken?
... is the answer already to your own question. Of all the proposals anyone ever came up with (to my knowledge), you can satisfy two of the following three conditions, but not all three of them at the same time: secure, decentralized, for free
*.
There's maybe a discussion to be had if PoW is the final correct choice for the main player in crypto (Note: I still think it is, roughly, because of hardware cost binding miners to the blockchain, and only one blockchain at a time), but that's more specific already than the objection to your idea:
Describe please how a decentralized ledger without a native token incentivizes participation?Sure, participation (of miners) could be funded by outside capital, but then the question becomes, how to distribute it? How to see which outside actor has which share of the funding? Such a system sounds a lot like political party funding in the US, and I would describe that as 'partisan' and 'toxic' long before I would use the term 'decentralized'.
In the end, any proposal I've heard or can come up with myself either violates the decentralization constraint, or it becomes so complex that it essentially recreates the native token system of the blockchain. But that one exists already
* I know, the point can be made (and would be correct) that e.g. a centralized system like Visa is anything but cheap. The point is, in principle, if security rests on one entity with absolute power, this removes the broader system of financial incentives you need for a decentralized setup like crypto.
Well even if we don't have today a network that works fine without a native token doesn't mean that it won't be built in the future.
But actually, these technologies are starting to appear.
Eris industries claim that they can build blockchains to be used for smart contracts without any cryptotoken at all and that anybody can use them today, right now.
https://erisindustries.com/Then we have Ripple and Ethereum where the tokens "are there" but more as a anti-spam mechanism, meaning that the network is not dependent on the token (token is not necessary to be used by participants, is not the main point, and its price can be whatever, as opposed to bitcoin in the bitcoin blockchain).
So the trend seems to be cryptocurrencies -> distributed ledgers.
Where the tokens (the cryptocurrencies) are less and less relevant and necessary, until they are not even needed at all.
You say that you haven't found a proposal that doesn't violate the constraints "decentralised, cheap, secure".
Ok for "secure" or "cheap", but regarding "decentralised": Why does the network have to be 100% decentralised?
VCs, banks or whatever are interested in bitcoin and crypto not because it's decentralised, but because it allows fast, global, cheap payments (at least that's what they think, because it's not that simple...) and allows applications like smart contracts and all that. Decentralisation is only one way to get there.
If some components of the network are centralised, it's not a problem, and it might even be preferred by them.
In the end it all comes down to what the world will find more useful and what it will actually adopt.
100% decentralisation has more to do with ideology than actual usefulness IMHO.