The human crew isn't much of a factor in cargo ship speed. Ship owners would be happy to leave their crews out at sea a week longer if it was profitable.

Drone ships won't be practical any time soon because of maintenance problems. Crews spend much of their time at sea performing preventative maintenance, painting, and fixing broken equipment. With a drone ship all of that work would have to be done at the pier which would be far more expensive than paying a crew.

Then why don't they go slower? I would expect many cargoes aren't incredibly time sensitive.

They are already slow steaming on many routes. Ship owners aren't idiots; they have software to perform constrained optimization calculations to figure out the steaming speed which will maximize profit on each leg. This is based on fuel price, crew wages, asset depreciation, delivery contracts, etc.