That’s a weird question. Of course people play and enjoy fighting games. Do you mean do new players play and enjoy them? Fighters do get new players all the time. Most don’t enjoy it if they are just jumping online and trying to win. They lose badly and get frustrated. You basically need to know what you’re getting into with the genre. Most people are used to popping in Halo, CoD, GTA, or some other popular game, jumping online, and having some fun for an hour or two. That’s not what you should expect with a fighting game. You will be against people who have hundreds to thousands of hours playing against real opponent online. The genre has a high skill ceiling, so that means they will likely be somewhere above your skill level. It’s not a rule that they will win, but you should definitely accept it if they do. And even if they don’t have more time invested than you, you also have to accept that some people learn stuff at a faster rate than others. Or maybe they spent most of their time learning one effective gimmick that you can’t deal with.
I think the people who enjoy it most are the ones who know that it’s a marathon, accept their losses as they come, and view them as a learning experience. It’s really easy to say “that guy only beat me because he was spamming that move,” but that scrub mentality will make the experience worse for you, and it robs you of the lesson you should be learning. It’s far more effective to instead accept that you failed to counter that move, and then go into training mode or look online at how to counter it.
You don’t need an arcade stick these days. Fighters have gotten very easy when it comes to execution. Much of the pro scene for Street Fighter 5 are pad users. However, sticks have some benefits. They wear out much less over time(assuming it has Sanwa or comparable parts), and if a stick or button does fail, you can easily and quickly swap in a new part yourself. They also feel more consistent from platform to platform. For example, a PS4 and Xbox One controller feel nothing alike. There are alternatives though, like the Fightpad and Fighting Commander.
You don’t really need a mentor with all the guides out there, but, it’s good to play better players who can tell you what you’re doing wrong in a match. Sometimes you won’t realize what you’re doing wrong, so playing someone who can tell you to stop jumping or just block and stop pressing buttons when you need to hear it is helpful.
My suggestion for a game to start with is Street Fighter 5. It has the most new players and there are tons of guides for it. Gief’s Gym is a great guide for new players, and there a loads of youtubers who are dedicated to fighting game videos as well, like UltraChen, Vesper Arcade, JM Crofts, and many others. SFV also has easy combos and very lenient move input requirements.