Hydrogen from syngas (thus ammonia), sulphur (thus sulphuric acid), ethylene, benzene, and so many others, they’re used for absolutely everything: fertilisers, medication, explosives, solvents, detergent, dyes. Even a good chunk of the industrial ethanol comes from ethylene.
And as you hinted, plastics. We still need them for water tubes, computers, and everything else.
So even in a future where we stop doing stupid shit like literally burning old dino juice, and we reduce the amount of plastics to reasonable levels, we’re still going to need petrochemicals.