In Tasha's Cauldron of Everything (and the preceding Unearthed Arcana), the Eldritch Adept feat (p. 79) lets the character learn one Eldritch Invocation. However, it has a prerequisite: the Spellcasting or Pact Magic. Hence, it excludes only non-EK Fighters, non-AT Rogues, Barbarians, and Monks.
I understand the thematic reasons for this prerequisite to exist, but are there game balance reasons for it? That is, would it be unbalanced to allow non-spellcasters to take the Eldritch Adept feat? Answers should include example class/invocation synergies.