I just installed a polarizing lens filter on my 150-600mm telephoto lens last week. This week, I was photographing birds by boat when my camera strap slipped off my shoulder and fell to the deck, lens first. I tried the camera out, and it seemed to be shooting fine, despite the cracks.
I just got home and took off the filter and the lens is fine! My relief is palpable. If you have been putting off adding a filter to your expensive lenses, I really recommend it.
I used to use entirely clear filters (UV blocking, perhaps) purely for protection. After seeing various debates I swapped over to religiously using a lens hood, regardless of whether there was glare making the hood needed for its actual purpose. I think the argument was that hoods protect against a wider range of impacts, and in particular provide some cushioning, while filters obviously have an optical impact even if “clear”. Third party hoods are also cheap.
That said, hoods are bulky, so filters as protection have their place.