I suppose, at the end of the day, to bring fighters up, the magic items you give have to be things that allow for out of combat effects. It's not really an issue in combat - and that's largely why older versions of D&D got away with it - no one had any real abilities out of combat. Not really. The casters just didn't get enough spells, and, if you go to really old D&D, the spells just didn't exist. I mean, a Basic/Expert MU got, what, six, eight spells per level? I don't mean spell slots. I mean that there were actually only six or eight actual spells per level. So it wasn't like the MU was rewriting the game very often.
But, since 5e allows for a pretty broad spell list (much truncated from, say 3e, but, still pretty broad and gettin broader every year), we'd need to give fighters/rogues abilities that are just as broad. Mjollnir lets Thor fly, after all. That sort of thing. The problem, as you say, comes with limiting who can take the items. Because if the items are free to use for everyone, well, why would I give it to the fighter and not another character?