The great filter isn’t about FTL. It’s about life or intelligent life. It’s a theory about why we haven’t met any other species, sure, but you don’t need FTL to populate the galaxy, all you need is time. And apparently, the math makes it clear that even with fairly slow travel, the time the galaxy has been around is enough for a species to colonize all of it.
The theory says that intelligent life that survives long enough to reach us is basically impossible. Maybe it’s because life itself is basically impossible. Maybe it’s multicellular life. Maybe it’s our kind of intelligence. Maybe it’s technology.
Maybe the great filter is behind us. Maybe we’re the lucky ones who managed to avoid the filter, the longer we fail to find any kind of life, the more this makes sense. But maybe the filter is just around the corner for us, nukes, nano something, just general fucking up the planet with tech you barely control…
And people already explained it… :D