No Hosta ever *needs* to be divided. You can choose to divide it because you want to propagate it or because it has gotten too big for the spot that it is in. But division is never required in the way it is for other perennials. It will set plants back into a more immature stage of development.
In the case of the fairy ring or dead center of the Hosta as first presented, if you didn't want to move it you have two choices. 1. Leave it alone and it will leaf out into a nice looking clump. You will never notice the bare spot in the middle except for in April. My mother had several plants of Undulata Erromena that looked exactly like that top picture. She had them for decades. They looked great all summer long. 2. If the middle spot bothers you, you can take a narrow spade and dig out the dead middle part of the clump and replace it with compost. The Hosta will then grow into the middle of that donut in the years to come. My preference would be to leave it alone, unless you want to move it.
The professor is right on a couple of points. Alfalfa is a great balanced organic fertilizer for Hosta. But don't use the pellets. Those are bunny food. Alfalfa meal either scratched into the soil or watered in will do fine. If you've got a bunny or deer problem, try Milorganite (5-2-0). It will keep the critters away for at least a month while it provides an organic fertilizer. Secondly, that picture doesn't look like a four year old plant, as the professor says. But I don't think it's because of a lack of fertilizer. The plant shows an awful lot of growth for that age of plant. It could be that this plant received an excess of nitrogen from the fertilization of the lawn around it. Grass fert is often something like 32-0-4. That excess nitrogen will cause lots of leaf growth but not much root growth. In any case the alfalfa meal will solve the problem.
Just remember, never divide, unless you want to.
