Going by that description (I'm otherwise a n00b), my guess is that only a fraction of validator slots would be active, which means the network could be easily hijacked by a well-funded party who just wants to see the network burn (e.g. central bank of a superpower).

Another possible weakness could occur if staking is mostly outsourced (i.e. staking as a service) and one provider overwhelmingly dominates the market. That provider would be in a position to hijack the network without having much of a stake in it. Proof of stake doesn't really live up to its name if the validation nodes aren't run by validation slot owners.