For those unfamiliar with the term, "breaking" a game essentially means finding some combination of skills, items, etc. that completely and utterly trivializes any challenge the game might throw at the player.
For example, in Octopath Traveler the combination of the Runelord class and Tressa makes physical enemies a joke, as by using Transfer Rune followed by Sidestep Tressa can make it so every physical attack thrown at the party misses. This particular combination isn't the easiest to lock, however, as the Runelord job is locked behind a powerful boss. However, Octopath Traveler has another, more easily accessible example in the form of the Hunter job's Leghold Trap, which forces the target to move last for a few turns. Coupled with the game's Break system, there's a good chance most bosses will be spending the battle unable to move and thus not that much of a challenge.
A more general example is good old level grinding. At a high enough level most enemies will be hard pressed to really threaten the player, so by taking some time to gain some more levels the player has the means to easily get pass most of the game's challenges, at the expense of time (level grinding generally takes a while).
From a gameplay standpoint, completely and utterly stomping a game can be really fun. A lot of players get a kick out of it, especially as a reward for completing something time-consuming and/or particularly difficult. From a developer's standpoint, however, such an outcome may not be so desirable. After all, it can be seen as not experiencing the game in a way the developer intended.
The question is: how easy should it be for the player to obtain game breakers? Should it be possible at all?
My opinion, realized as I was typing this, is that the best game breakers are actually the ones the developer intended. If the developer is really clever about implementing them, the player stumbling upon them randomly can actually make them feel really smart for discovering it without actually realizing that it was intended all along.
Here's a good video to elaborate on it (it's about Terraria specifically, but it can be applied pretty generally as well).
Elaborating on that, I don't think game breakers should be that easy to obtain. Sure, it's all fun and good to make it possible to allow the player to break the game over their knee, and in all honesty I do think there should be options for the player to make the game easier on themselves. But there's a fine line between "making the game easier on themselves" and "making the game impossible to lose unless the player's a total dunce." An easily obtained game breaker that turns battles into "spam the game breaker and win" is likely to make the game really boring.
Ultimately I also think it depends on the demographic the developer's aiming for. People who want a challenge probably won't appreciate a game dropping a game breaker on them with little to no work required, but people who are looking for a more casual experience might appreciate it more.
I'm only one person, though. What's everyone else's opinion on the matter?