In reality, Exist.
In the broader context of fantasy? All sorts of things depending upon any consistent rules that have been established or inconsistent author force that has been applied. For a completely off the wall example, in the short-lived 80s comedy, Wizards & Warriors "wizards can't kill" ("true, but we can put you to sleep for 1000 years!").
In D&D, specifically, there's basically nothing non-casters can do that casters can't. Especially in 5e, where every class has at least one class that casts. True, in the classic game there were outright proscriptions, and Wizard or Cleric literally /couldn't/ use a sword, but they could both still attack with a weapon, so it's just something they couldn't do as well, not something they couldn't do at all.
Magic /can/ stop magic from working, tho, counterspell, dispel, anti-magic, etc.... which is something not-magic can't do... and the mage in the anti-magic zone can't cast spells or use magic items, but neither can the fighter.
In 5e, they have at-will spells, and slots(+HD) represent more endurance for such days than (slightly larger)HD, alone.