As there is no rewards, there are no strategies apart from trying to double spend, and the odds that you can do it because you happen to be the preferred staker on the false chain are small.
What about censorship?
@dinofelis you've made one correct step towards my design. Congrats.
There are many more details to reach a viable system with the desirable qualities.
My design may not look at all like what you just described, but abstractly it is.
The problem I see with minimal or no minter rewards is that minters wouldn't lose much by not mining (or only mining on top of selected blocks), which lowers the amount needed to bribe them to perform any action desired by an attacker.
How does your system protect against bribing attacks? (In my proposed model, the big number of anonymous minters guarantees that an attack must be made public before it has started.)
There seems to be a real tradeoff tied to block rewards: They should be as small as possible to avoid selfish mining strategies (and economies-of-scale) and as large as possible to make bribe attacks costly.