Game play quickly reveals it. Broken things can't be kept secret and aren't hard to spot when they rear their ugly heads. There's simply no need to know every nook and cranny to recognize when something is broken in play.
In my experience?
No, no it does not "quickly reveal it", unless it's something so
horrendously stupidly broken that even the person DOING it will usually admit how broken it was and accept that it was a one-time-only thing.
Instead, for the vast majority of it, it builds up slowly, one brick at a time. Every brick seems reasonable, if granting some little bit of power. And by the time you've realized what's happened, there's an entire wall of precedent that now DOES actually result in the player having a legitimate grievance if you do something about it
only now, months and months after they started building their character.
Worse, the vast majority of fixes end up actually being such massively punitive nerfs, you've basically taken the player's character away. So you're damned if you do, damned if you don't. If you didn't catch these 7 slightly-OP things a year ago, you're now stuck with the choice between ruining the most successful player's experience, or making everyone else feel like dead weight because the one hyper-optimized artificer (or whatever) solves multiple entire challenges single-handedly
every single day.
And, yes, some of the very broken things absolutely come from splats/supplements. Spell-to-power Erudite, for example. But none of those things is
radically stronger than Druid + Natural Spell; they are at best very small upgrades over it. A smartly-played Druid, even stuck with only the PHB, is an absolute monster.