Of course, the converse does not follow: a chef who doesn't eat good food, and a writer who doesn't read much (or who reads nothing but the worst trash), is not likely to develop much skill.
But we're not talking about the converse. The point is, just being a Trek fan doesn't make you a good writer.
What you're talking about is just the starting point. It's what creates your interest in developing the skill. It's not training in itself. I was an avid consumer of science fiction for maybe 15 years before I started trying to write it professionally, and the first things I wrote were pretty bad. What made me good enough was the subsequent 7 years of actually
working at it, writing stories and learning from my rejections and striving to raise my game, learning the craft and the technique and the difference between what I personally liked and what lived up to professional standards. It takes hard work, a
lot of hard work, to become skilled, and fandom is not work, it's recreation. It's only when you
stop settling for being just a fan and start to approach it as a profession that you even have a chance to become any good at it.
And I never would've become a good Trek writer if the only thing I was a fan of was
Star Trek. Trek itself is a distillation of decades' worth of earlier science fiction concepts and traditions, plus other outside influences like Horatio Hornblower, Shakespeare, etc. It takes wide experience to be good at doing one thing, to learn a broad enough range of influences and inspirations to let you add something meaningful to a series rather than just rehashing what it's already done. The fact that Marshak & Culbreath had no writing experience
beyond Trek is probably part of what made their writing so clumsy and self-indulgent.
So I repeat: There is absolutely
nothing ironic about M&C being both the biggest Trek fans and the weakest writers. Irony is when something is unexpected, and it is invalid to
expect fandom to correlate with professional competence.