Hardcore mathcraft time.
In general the game was actually designed so that magic and physical got better via different means. Physical theoretically has a better multiplier from stats (damage proportional to 1.8th power of ATK vs 1.65th power of MAG), while Magic theoretically has a better multiplier from higher ranked abilities. This kind of mimics logic, I guess, where how hard you punch or swing a sword has a lot to do with how strong you are, and how hot a fire you magic up has a lot to do with what spells you know.
However, they messed up all the meta maths by making the gap between ranks for magic far outscale physical. ATK and MAG also have soft-caps which massively hamper physical, because by the time you get to ATK levels that really make the higher equation shine, you're already well into soft-cap territory. (This was adjusted at different points in the release timeline in JP and Global - more on this later)
This actually means that in practice, mage meta is actually less gear dependent than physical if your abilities are good (like, you have enough orbs to hone 4* magic a few times, Meteor, etc). Mage meta 'works' with non-RS 5* rods because of this, where for physical you need a 5* RS sword to do anywhere near decent damage.
Two things to consider that contradict the above (both in large ways)
1) As mentioned, you need a baseline of good mage gear to start off, which takes months depending how lucky you are from when you start the game. The only thing is this is largely realm-agnostic (RS is definitely a bonus, but hampered by 9999 cap) so whatever mage gear you get sets you up for any realm.
2) Advance and/or Retaliate drastically reduces the offensive gearing requirement of a 'physical' setup by requiring only one good weapon per realm. This, for all intents and purposes, puts the gear requirement before that point in 1) far lower than magic setups.
Retaliate basically breaks the game in terms of gear req, but it takes a ton of turns to set up and maintain, meaning there's an inherent 'upkeep' to it that's not insignificant. Despite being able to double cut massive numbers, this turn tax actually puts Advance/Retaliate with a 5* RS around the same offensive output as a fully kitted out mage team with a ridiculous amount of ability hones.
Physical pulls ahead when gearing gets even better (back to the whole physical = stats, magic = ability ranks design) because when you aren't relying on Advance any more, things like Planet Protector, Deprotectga, and a bunch of other interchangeable RWs that boost entire party's ATK or decrease entire enemy's DEF means virtually everyone can hit for 9999 even with 4* RS weapons, making the party do equivalent damage to a mage setup BUT bringing debuffs (breakdowns, status busters, etc) into the equation.
As an addendum, when people say "mage meta dominates", they generally would be referring to the period of Month 4 to Month 7 of the Japanese service, where a magic setup would literally do twice as much damage as physical. That all changed in Japan with the release of SSBs, things like Planet Protector and the raising of the ATK softcap. Over on the global side, we actually got the ATK softcap changes early, so we didn't have that same months-long period of go-mage-or-go-home, but magic was still measurably better for a while. On Global we're now past that Month 7 point where characters are going to lv80 and we got the first of our party ATK buffs with Planet Protector, so mage meta is rapidly falling out of its leftover advantage.