If you replicate an existing system, but not as well, or you produce a game that no-one wants ... it's not going to find an audience. If your goal is a vanity project, sure, go for it. But if you want to find an audience, you need to work.
That's easy. Yes, you must read a lot. If you don't understand and appreciate good writing, your writing will be bad.
I disagree.
I mean, yes, engaging as a reader can help you become a better writer. I would hazard a guess that very few writers are not also avid readers anyway. But should I track down the "important" or "classic" novels in the genres I want to write in, before I get seriously started on my own writing? It's not a bad choice, but also not a necessary choice. It would be easy to get lost in "preparing" for my craft as a writer and never actually getting started. Once I have started . . . I'm going to continue being a reader, and I probably will look to pick up some "classics" that I haven't already read, or would like to read again.
As a game designer . . . I'm not a fan of the term "vanity project". But it is important to decide what type of game design you are interested in doing. Do I want to create my own game? Do I want to create supplements for existing games? Am I fine creating design for D&D 5E only on the DM's Guild for beer money? Or do I want to make a living at this crazy profession? Those choices will inform how much I might want to study other games.
Like most writers being avid readers, I would assume that most aspiring game designers are avid gamers! Although, just like a reader can get stuck in one "comfortable" genre, a gamer might only play D&D or a small handful of games. Which is okay. If I am obsessed with D&D and really are only interested in creating products compatible with D&D . . . again, it can't hurt to become familiar with other game designs within and without the D&D-sphere, but hardly necessary. If I'm interested in someday creating my own game . . . it would benefit me more to study some of the more well-received games out there. But don't wait until you have studied all of the "important" games in depth . . . get started designing! And study games that interest you along the way, either from a genre or design perspective. Or because you want to play them with your local group!
Producing a poor quality game, or a game that "no one wants" is always a danger, no matter how many other games you've studied. I'm not worried about "replicating an existing system", well or poorly, plenty of games out there have both intentional and unintentional similarities, which is independent of quality.