Yes, in fact it's part of my confusion. The layer object in the link you posted (thanks!) includes the .disableTime() function, so presumably that method can be called on a layer returned from listLayers() of the project map. When I use the method it does nothing (see the first screenshot) in my original post. I may be missing something obvious.
Looking closer, I see that the isTimeEnabled property is read-only for layer, it's read/write for MapTime, so my second screenshot shows the expected behavior.