EVERYTHING IS ARBITRARY IN A GAME
I don't know if you're saying this because you're just angry and overreacting, or if you genuinely feel like you could back it up, but I strongly disagree.
Certainly, the premise of the gameplay could be arbitrary by some estimates, but it's usually based on appealing to a niche set of preferences, and mechanics evolve to accommodate those preferences.
Take Smash for example. The premise is a platform-based fighter with ring-outs as the sole win condition. Now that's certainly a narrow definition, but it's turned out to be a pretty successful niche, and the lack of viable imitators means Smash pretty much has the market cornered (although granted the initial draw is the source the characters are drawn from). Regardless, from this premise several things arise as necessary. Movement options need to be broad, since the multi-level gameplay and large stages are otherwise invitations to turtle to an unbeatable degree. This is why action game elements like short hopping and drifting are included. Double jumps are ported from airdash fighters for this purpose as well. Melee expanded on this with platform wavelands, wall-jumps, dash-dancing, fox-trotting, ledgecanceling, etc. Compounding knockback returns also arise to reward the winning player with a greater likelihood of achieving the win condition. Core fighting game mechanics are included to make the combat deep, like grabs, rolling, crouching, specials, blocking, hitstun, blockstun, etc. SDI in the first game was included to counteract long combos, and Melee expanded on the concept, making it more interactive and intuitive, and giving it a more direct interaction with the win condition. Recovering is an emergent mechanic from the non-arbitrary mechanics of drifting and double jumps. It would be there (and in fact is there) whether the characters had recovery-oriented specials or not. To make recovering more viable, and balance survival based, defensive gameplay with aggressive, gimp-oriented gameplay, the ledge mechanics are introduced. And everything from the ledge is either emergent or serves a purpose.
Originally, L-canceling was intended to allow players the choice of hitting with the landing hitbox of a move, or initiating their defense off a whiffed attack. Note that defense was the intended purpose of l-canceling. This is where you really have to remember that Smash is an ongoing experiment in previously totally unexplored gameplay territory. L-canceling was an experiment, and the conclusion was wildly different from the hypothesis. L-canceling became quite the monstrosity, evolving from a mix-up between offense and defense into a required skill-based barrier to offensive play. Melee even went so far as to remove the mix-up aspect and allow the arbitrary utility of the mechanic to take front and center. Now it's nice to look at the history of l-canceling and observe that it wasn't intended to be arbitrary, but a synchronic appraisal of the mechanic shows that it's simply an extraneous required input to perform a successful aerial. That's bad game design. It doesn't really matter if emergent qualities of the game make it deep, because it totally fails to balance accessibility with a plurality of options (and yes, accessibility is a goal).
It's the balance of accessibility and option plurality that I'm really in favor of, too, and it's why I don't necessarily support the outright removal of l-canceling (since that would sacrifice option plurality for accessibility). Instead, making l-canceling cost some other valuable resource balances the extra option of l-canceling with allowing the player who can't l-cancel consistently to save that valuable resource toward some other purpose. Incidentally, this is why meters are so pervasive in other fighting games, since they're a quick fix to the conundrum of balancing accessibility with option plurality. It is the disregard for this balance that makes l-canceling arbitrary. And it is the consideration of overall balance, including this particular field of balance that makes the other decisions in game design non-aribitrary.