I think that a lot of things that we call procedural really aren't.

Procedural comes from the term process, but a lot of people feed random numbers in and call it a day, like Skyrim's Radiant quests. Yes, there's some setting considerations going on, but it doesn't feel distinct from rolling a die and seeing which cave the bad guy is in.

Really good play happens when complicated systems interact in ways players don't necessarily expect, but which they can intuit. If there are fewer people out because of bad weather, which means that the police chasing the bank robbing players (because, let's face it, players love causing chaos) have a clear shot and don't have to worry about collateral damage, that's a meaningful distinction that isn't necessarily transparent.

Many games love shouting and hollering when a system like that is in play. It's in little details, however, that you can create a unique experience.

Likewise, to tell a story you really don't need a human at the wheel (though I do hope to one day become a novelist, so I should be careful how much I say that), because these complex and interconnected systems are stories in their own rights. They can have characters, outcomes, and plotlines that resemble stories that have been hand-crafted, because the system increasingly reflects reality and stories are a means of talking about reality. There's some aimlessness, sure, but there's also room to find purpose where there was previously only entropy or a void.