I guess one has to choose being mediocre at many games or being a grandmaster wizard at one game. Maybe I'm wrong, maybe one can master many games in a short period of time. I'd like to think this kind of gamer is a myth
There are some who play only one game over and over for competitive purposes. Eg, mastering RTS's is often all about developing muscle memory for keyboard shortcuts, memorizing counters, etc. However, not going to that extreme of spending 40hrs per week of doing that hardly means the opposite of being "mediocre". If you've been playing a variety of games for years then you will inevitably build-up a kind of "muscle memory" skill-set for several genres and simply won't be "mediocre" at anything. Eg, growing up with the early Thief games means you'll probably be "pretty damn good" picking up Dishonored / Styx: Master of Shadows stealth / assassin style gameplay even during the first playthrough. Likewise, it's not like you'll be "totally mediocre" at ARPG's if you replayed Diablo 2 & Torchlight a dozen times, or "utterly clueless" at The Talos Principle if you can't get enough of Portal, Quantum Conundrum, QUBE, Magrunner, etc.
As far as MP shooters are concerned, I grew up with the faster-paced arena shooters of the 90's (Doom, Quake, Unreal, Serious Sam, ROTT, etc). Since most FPS controls are fairly similar to each other, even today I find that "honed twitch response" means being pretty good at FPS's in general despite being 20 years older. Having said that, I also find the "being the best in the world" rat-race of modern MP FPS's tedious due to formerly
player-centric mechanical skill development (ie, developing near pixel-precise mouse placement accuracy which transfers across FPS games) being replaced with
game-specific-grind centric mechanics that starts from scratch for each game involving "levelup boosts" via rankings / unlocks / pre-order "bonuses" /
permitted cheat-mode enlarged hitboxes or auto-aiming for players using controllers instead of K&M, and "see through wall HUD's and overlay maps" not to mention the Godawful rise of pay2cheat / pay2levelup cr*p or pervasive chronic cheating. In that respect, modern games will need a lot more "grinding" simply because they're specifically designed to be a grind-fest to subtly 'encourage' more P2W micro-transactions vs "strictly equal footing" of "rank-less old school" arena / twitch shooters.
I really wouldn't worry about not having the time / interest to master every single game or becoming #1 on the planet for any given game (which often involves that person having no life whatsoever outside of +50hrs per week of that game). The bottom line of gaming is to have fun and overdoing the grind-grind-grind can often end up anything but that. If anything I would say playing a variety of games reduces the likelihood of getting "burned out" on a genre / style of play, and ending up not playing them at all for a while.