As I understand it, the ring amplifies the users power. If everything else in the world works as additive and multiplicative modifiers, the ring is exponential and based on your desires. Wizard is already very powerful and already has a lot of desire for change in the world. Wizard² is going to be a huge number. Man is shown to always be ravinous for power and control man² would be so much more so. Hobbits live an idealistic life with all their needs met. Their biggest desires are a second meal and a neat Firework display. Hobbit² would just be eating the last breadstick before everyone else got one. We see that in Gollum, who was willing to kill for the ring but content to just use it to catch fish in a cave for a century. Exponential power means nothing if your needs are already met.