Right now our current science tells us FTL is impossible (but we're working on it).
Nope, our current science tells us FTL is not only possible, we even know what we need to do in order to it. Now how to actually practically do it, is the only hurdle.
Why is it silly? We live in the 21st century. We're discussing 21st century entertainment. Why would it be silly for anyone to want to see a piece of entertainment that, while set in the future, still reflects and conforms to our current level of understanding?
Second, you want to use present understanding of science ALONE to describe a far future setting, where our understanding will have changed, probably a lot.
So this pining for "scientific purity" is kind of silly.
Someone mentioned literature. There are numerous books out there that deal with science fiction in a more "hard" or "scientific purity" fashion. I'm reading Ben Bova's books at the moment. I've completed most of the "Grand Tour" series of books. It's great. Hard scifi completely set within our own solar system. No mental powers, no supernatural beings or cosmically advanced aliens.
On the other hand wanting or asking for some form of "scientific purity" doesn't exclude scientific advances unknown to us.
Let me illustrate. In the 1950s there was an SF novel. I can't remember the writer, but the novel depicted desktop computers on every desk, sometimes multiple in a home, faster than the fastest computer back then, and to top it off, all the computers were linked together in a world wide network. Sound familiar?
You know what the going scientific rate was on the book? It was ridiculous! Computers could NEVER intercommunicate. And Computers would NEVER get smaller, they'd only get BIGGER! Sure as science!
Less then twenty years later, the first desktop computers arrived. Another dozen years later and the European universities and soon after American universities got connected in the first global network. Another fifteen years later and the world wide web was born. Another ten years after that, and here we are.
THAT is why artificially keeping yourself to what "present day science" tells us is rather, well, ridiculous. What scientists would tell you is impossible today, and won't happen in a million years, might be on your desk no more than a decade later, and your children would laugh the scientists who told you it was so impossible out of the building.
The same happened with Jules Verne's envisioning of men landing on the moon. It would never happen! Then it became 1969. Ships traveling under water? Hah! Would never happen!
A good rule of thumb is; if Science Fiction shows you something that Science are hard telling you it's impossible; expect it to be true within your lifetime. Higher chance of that occurring than it being actually impossible.