system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: why do the Wizards in The Hobbit/LOTR rarely use their powers in combat, preferring to use swords?
gpt
Because they're not allowed to except in worst case scenarios. The movies do not explain it since it's not pertinent to the LOTR or Hobbit stories, but another Tolkien book called The Silmarillion explains that the wizards are essentially angels sent in human form to advise and counsel, not fight.

In the Tolkien-verse, there are various levels of supernatural beings. Eru Iluvatar is essentially God. He sent 12(13 at first) lesser beings called the Valar to Middle Earth at its creation to manage things. They would be like the archangels in Christianity, though more like Greek or Roman gods in that they can take human form sometimes, each is in charge of some various aspect of nature, etc. 

Underneath the Valar are the Maiar. Basic angels, servants of the Valar. Sauron was Maiar, as was the Balrog, and all of the wizards. Sauron, being evil, chooses to use his power however he wants. The wizards on the other hand, being good and still choosing to obey the Valar, are prohibited from using their full power by the Valar and were instead instructed to take human form. Again, their primary mission was to instruct and give advice. The War of the Ring was deemed by the Valar to be a problem created by the inhabitants of Middle Earth, and thus theirs to solve. The Valar refuse to take an active role in fighting the wars of Middle Earth, as they had in the past. But they still care for Elves, Men, and Dwarves, so their answer was to send the wizards. Not to solve the problem, but to help others solve it.

Not that you asked, but this is also the reason to the often asked "why don't the eagles just take the Ring to Mordor?" question. The giant eagles in LOTR are explained in The Silmarillion as essentially being the pets of Manwe (head of the Valar). They follow his command, bring him news, and are his favorite of the animals. It is likely that they were not allowed to solve the Ring problem on their own either.