It's a game rule, but was it ever mentioned in the show?
During XY, both Sawyer and Alain had 2 Pokemon who could mega (Salamence & Sceptile/Metagross & Charizard), but the situations where they used both only came up during the Kalos League. I don't think anyone else relevant had multiple mega-possible Pokemon + Mega Stones weren't exactly easily obtainable in the show (unless you're Audino but we don't talk about that episode). My in-universe headcanon says the Kalos League might have had rules against multiple Megas, but the real reason probably was to emulate the games. That being said, I don't want to watch all of XY again to figure out if they explicitly said anything.