Not 100% rodents, but the reason is simply this: Lizards in general have a requirement for a lower fat diet than snakes do. Carnivorous lizards fed only rodents may be prone to develop fatty liver disease. As a result, while rodents can make up part of their diet, it shouldn't be the only food they're given. Some of the largest monitors can be fed rodents as a primary food source, but keepers generally also offer ground turkey, earthworms, insects, cooked eggs, fresh fish (tilapia) and other items.

I had a green water dragon--he ate rat pups, mice, earthworms, zophobas, and flowers and dandelion leaves.
Monitor lizards eat a similar array of food, without the greenery. Some monitors can be given more mammalian prey than others. (The very large Varanous rudicollis should only be given insects, while Savannah monitors do well on a mix of insects and mammal prey, and big water monitors are often maintained mostly on rodents and ground turkey, with other additions for variety). In any case, it's better to feed fit, juvenile rodents to lizards, rather than chubby adults or retired breeders.