The reason why you aren't worried that all the PoW miners will go offline is that they're rewarded for their work. Similarly, if stakeholders are rewarded, then we can expect some fraction of them to be online. In section 3.2.1 of the paper we describe how to incentivize a target participation level of the online stake.
Ok, I understand why people would mine, that wasn't the question, but are you saying the system will automatically tune to 10 minutes for finding a successful block? I suppose it will just readjust based on the implicit(explicit?) fraction of BTC stakes, as well as the PoW being done?
edit: Reading the slides. While it's well-written, I'm always annoyed that in one breathe people are concerned that miners will mine empty blocks, but similarly we shouldn't worry about PoA stakers to not do it. They're both invested in the same system with equiv capital(theoretically). It's not a substantial difference. Otherwise, I'm enjoying the read. It's easily the most "believable" for a PoS skeptic like myself, for a number of reasons.
edit2: If we are capping value of blocks, will we have a rule that allows a single transaction block that goes over that limit? Otherwise you wouldn't be able to spend BTC at extremely large valued addresses. Would the cap value mean miners will just include tons of dust transactions? Or would the value cap be *in addition* to the 1MB data cap? Or are we hoping the size propagation penalty will naturally force this down? Would this also encourage people to split up their BTC into smaller value, increasing the UTXO set? Just random things to think about.