People play different card games, different board games, different video games, etc. So, when it comes to Chess, why would people limit themselves to one particular game of its type? Chess has built around it a structure of competitive play. People join Chess clubs, compete in Chess tournaments, and gain ratings and titles in the world of Chess. A narrow focus on Chess can develop when people focus on competition and the gaining of mastery. Outside of the world of competitive Chess, Chess is just a game, and the reasons for playing Chess often apply to Chess variants too.
Chess is a game that requires abstract thinking and forethought. This is a general quality of abstract, strategy board games. (see What is a Chess variant?) It is part of the appeal of games like Checkers, Go, and Othello. But if you find Chess still more appealing than these games, Chess variants offer you some more variety in abstract, strategy board games without losing the main qualities that distinguish Chess from these games. These include such qualities as a diversity of pieces, the object of targeting a single piece, and an abstract simulation of warfare. With Chess variants, you can try out different pieces than are found in Chess, boards of different sizes, shapes, or geometries than are used in Chess, and different rules than are used in Chess.
Although playing Chess variants might not hone your Chess skills as much as sticking just to Chess itself, playing Chess variants offers some advantages even in this respect. Playing Chess variants keeps you on your toes more. You can't fall back on knowing opening moves better than your opponent does. To do well, you have to be aware of everything that is going on and have a good command of Chess strategy and tactics. This makes playing Chess variants a good way to develop the intellectual capacities that help you play Chess well. And, in the end, what is really more important? The intellectual capacities that playing Chess helps you develop or skill in Chess? Personally, I consider developing my intellect much more important than mastering a particular game, and that's one of the reasons I consider playing Chess variants a more worthwhile pursuit than just focusing on Chess.
Also, winning a Chess variant is more a feat of intellect than winning at Chess is. It doesn't take reasoning abilities to memorize opening moves in Chess. Thanks to the detailed analysis of opening moves in Chess, which many books have been written on, someone with a good memory could easily defeat someone whose main strength in Chess is a keen intellect. Like Sherlock Holmes, I am more interested in intellectual challenge than I am in filling my mind with trivia. Knowledge of opening moves has no use outside of Chess, and the prospect of studying the literature on it seems too boring to me. I would rather venture into uncharted territory, as I do with Chess variants, than play a game where memorization gives someone a huge advantage.
One more thing is that Chess variants don't have the same culture of fierce competition that Chess has around it. In 1960, Robert Lauzon and Jim France had become dissatisfied with Chess clubs that focused more on winning than on friendship, and they started a correspondence Chess club called Knights of the Square Table, or NOST as it was abbreviated, which focused more on friendship and conversation than on ensuring victory. In time, the members of NOST began to frequently play Chess variants together. After all, when competition is no longer the key thing, there is more freedom to try out and explore different games. NOST died out as its members grew older, and correspondence play moved from postal mail to the internet. But the interest in Chess variants that had thrived in NOST found a new home in this website, which, with Game Courier, enables the friendly correspondence play of Chess variants.