Compost is always good. I did that -- at least 1" layer -- with my big patio containers and windowboxes this summer.
My other containers go directly on the ground and the grass grows around them. I don't mulch them but I let the grass grow to the height of the containers which shades them and keep the roots cool(er).
Oh, I DO mulch my avocados in their containers with their own dead and pruned leaves cut up into small pieces (to fit the container) because I read that this is their natural state and there is substance in the leaves that breaks down and leaches into the soil which helps to prevent root rot. Same with the bananas.
Also, my containers that winter indoors get watered with used coffee grounds and worm compost in the watering can. They also all have at least one earthworm in each pot. So by spring, they all have a layer of used coffee grounds and worm compost on the surface of the soil mix.