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.