Maytag washing machine with a smooth tub and agitator. When running, the agitator does it's thing and the clothes essentially sit there and barely move. A truly horrible machine. I frequently remove clothes after a normal cycle that are completely dry. They just surfed on the top of the load. If I dump detergent on the clothes instead of using the dispenser, the detergent will still be there after a complete cycle. Washer claims it has "low water usage" and less wear and tear on clothes. It achieves that by not disturbing the clothes with water or agitation.

Is it possible to replace the agitator or tub or both with an old-style agitator with fins or spirals -- something that actually agitates?

No part available . . . these new machines are what they are. They look like standard washing machines from the outside but that's where it ends.
Good luck