One problem at a time. Nobody ever complained that an edition "didn't feel like D&D" on the grounds of fighters making basic weapon attacks.
Traditionally, fighters take the spotlight whenever magic does not. That can be against golems, which absolutely cannot be hurt by any spells whatsoever. It can be against goblins, who aren't worth wasting a spell slot on, but might inflict serious injury if you were forced to fight them with daggers and slings. It can be against the Big Bad, who is still alive after the spellcaster runs dry; or while escaping the dungeon, before the spellcaster gets a chance to recharge.
You don't need an on-demand "highlight" button to take the spotlight. It's enough to remain consistent, while everyone else goes through their highs and lows.