If I was making a high magic fantasy setting, instead of trying to worry about balancing casters against non casters I would just make everyone a caster and then build society around that. I consider that to be one of D&D's greatest flaws. You are making a tabletop ruleset - which is supposed to be played by people, which means it needs to be balanced - and then you are trying to tell me that someone who can manipulate time and bend reality is supposed to be balanced in comparison to someone who can't? I almost feel like its a bad joke. From my PoV, if you want to keep immersion, you either need to have a world where everyone is a caster and then a "fighter" is just a caster who uses melee spells, then you can make a balanced world, or you throw balance out of the window and tell people, "if you want to play a fighter, just know you will suck."
As a writer and someone who dabbles a lot in designing my own roleplay systems as a hobby this is more or less the conclusion I came to as well. There are three ways to make a believable magic system in which all players are able to work on the same playing field without getting too gamey.
1. Everyone uses magic. This is the easiest option and the one I am most inclined to. Melee characters operate more like Shadowrun's Adept. Enhancing themselves with magic to superhuman levels so they can perform Herculean feats that rival the ability to shoot lightning from your fingers. There may be non-magical people in the world but they'd be commoners and foot soldiers, not the heroic adventurer sorts.
2. Make magic take a really, really long time to pull off. No cantrips. No instant fire balls. If a mage wants to summon a lightning bolt it is going to need a few minutes to prepare beforehand, leaving them vulnerable to a skilled warrior with a sword if they don't have some protections prepared. This, however, works very badly for an RPG. "I'll stand here and do nothing for ten rounds!" is not very satisfying even if it makes for great dramatic tension in a story.
3. Technology closes the gap. Another option I really like but one that isn't compatible with sword and sorcery style settings. This is another strength of Shadowrun as a setting. Guns equalize things. Even if you're a mage with incredible power you can still get shot in the head and die. A normal person with no magic can enhance their physicals were cybernetic upgrades and wield explosives and firearms if they intend to go up against someone powering themselves with magic. I'd say a cyborg with a plasma cannon for a right hand is a pretty even fight for a wizard that can shoot lightning from his fingertips.
