...is Gentoo large and influential these days? As far as I'm aware, its current cultural status is that of a punchline, but I'm open to being corrected.
Gentoo is often at the forefront of identifying and helping resolve integration issues between different software projects, particularly when it comes to compiler tech (e.g. fixing packages so they can be built properly with LTO, or with LLVM as well as GCC) or other backend-detail-minutia which makes the whole system better without always being visible to the end user.