For similar reasons why competitive players like Pokemon.
Pokemon's stats are pretty stagnant (at least at a competitive level), with maximized IV's/EV's. You get the occasional abilities and natures that would be preferred in some instances over others, but for the most part, the Pokemon in question is always going to function uniquely in comparison to other Pokemon, but rarely will it ever change how it itself functions. Just going by this, some Pokemon are simply better than others due to their stats. Or at the very least, the matchups that they might have with one particular Pokemon will always have them at an advantage, yet a matchup they have with a different Pokemon might always have them at a disadvantage. And even with the best ability, IV's, and EV's possible for this particular Pokemon, they will always have this advantage/disadvantage relationship with other Pokemon that rarely ever changes.
...that is, until you throw their 4 moves into the mix. (Or Items/Mega Stones but that's a different story)
Depending on what 4 moves a Pokemon has, they can suddenly turn unfavorable matchups against a certain Pokemon into favorable ones. However, it could also come at the cost of losing potential favorable matchups against another Pokemon, because they changed their moves to be more suited to dealing with other threats. Some Pokemon, depending on their moves, become really really good depending on the 4 moves that they have, and end up having little to no checks/counters because of the 4 moves that they picked. Sometimes whenever a new Pokemon game comes out, and an old Pokemon can suddenly learn a new Move Tutor Move/TM/Egg Move/etc, they can shoot up in viability in the tier list because of this.
An example of this being Greninja: Already an OU competitive Pokemon that was sent to Ubers because it obtained Gunk Shot and Low Kick in Omega Ruby and Alpha Sapphire. Because this allowed it to get past Fairy Pokemon and Chansey/Blissey, things it used to have problems against before in X/Y.
http://www.smogon.com/forums/thread...utant-ninja-turtles-greninja-is-uber.3525033/
While the Custom Moves in Smash 4 might not have nearly the same impact as the 4 moves in Pokemon do, it doesn't have to make a huge impact in order to add more depth, variety, strategy, unpredictability, balance, and more in regards to competitive play. Because regardless of how good Custom Moves are, they provide options. And when there's more options, it always opens up the doors to more possibilities.
They can be thought of as tools. Not all tools are suited to the same tasks: Hammers, screwdrivers, wrenches, etc do better at doing certain tasks than others. But when it comes to their intended function, they are incredibly useful. And the more tools you have, the more tasks/jobs/etc you will be able to do with much more efficiency. Because I would much rather have a bunch of tools at my disposal to fix a car than to do it with my bare hands.