Sounds wrong. Slashing is a means to prevent people from staking on multiple chains. In PoW, computing power is scarce, so if you allocate some compute time to one chain then you have less of it on another chain. You automatically get slashed. The difficulty in designing a PoS chain is in artificially re-creating this slashing and thereby solving the "nothing at stake" problem.
The splitting is unavoidable and happens constantly. Multiple competing future states are constantly being created, and the network has to eventually arrive at a consensus about which possible future is the true one.
> Where is the difficulty in making miners expend their tokens (i.e. in a way that is irrevocable) instead of merely depositing them somewhere?
Figuring out how to make spending your tokens irrevocable is the whole point of PoW/PoS. Your question reads to me like "In trying to solve problem x, why don't you assume that you've already solved problem x, and use that to solve problem x."
Maybe I'm missing something... if miners are required to send the tokens to an invalid address, are these tokens not lost irrevocably?
This has a clear answer in PoW, but not in your scheme
An equivalent attack wouldn't work on a PoW chain. If you do the equivalent of "staking" on chain 2, then you're computing hashes, which is costing real-life resources. In the PoS case, without slashing, staking on chain 2 is free. In fact, this is the rational move to make every time you spend a token; stake on competing chains to get your token back.
There was a PoS mechanism that makes people who cheat lose all their coins? I wonder if it is relevant here
... Aha, that's "slashing" -- the other members in the network would look at the two chains, and notice that you were misbehaving, and add transactions that remove parts of your coins? (They'd add to both chains? Or just the winning one?)
PoS staking is simply committing a portion of your capital to the task of validating transactions. You benefit by receiving a reward in the form of additional tokens.
In a PoW system, the same exact thing can be accomplished by using your tokens to purchase a stake in a mining pool. You will similarly be unable to access your capital, be rewarded with additional tokens, and at the end of a period of your choice, you can liquidate your position in the mining pool to reclaim your tokens.
[edit] PoW in this context is a bit worse because PoW miners can rent out their hash power maliciously without being slashed.
In this world, the "nothing at stake" problem also manifests in proof of work, where I believe ownership in the mining pool makes you agnostic to the outcome of any chain splits - although I'm still working this bit through in my head. Opinions welcome!