I use one because I want to, because it completes the weather sealing and so that I can just wipe my lens down with my shirt without worrying about anything.
First of all, no Canon camera or lens is "completely weather sealed". Some models are more moisture and dust resistant than others, and installing a filter on certain lenses when out shooting in a dust storm or a rain storm can modestly improve their resistance to intrusion of moisture or dust. I just wouldn't get too overly confident. These cameras and lenses are far from being thoroughly sealed and need to be given reasonable protection in nasty weather... even if it's just a plastic bag, some rubber bands and gaffer tape.
IMO their "recommendation" about adding filters to some lenses to "complete weather sealing" is just Canon's way of selling more highly profitable accessories. Considering their guality, Canon filters are very overpriced, maybe double or triple what you'd pay for a Hoya or B+W of equal quality. Almost certainly Canon filters are outsourced and they don't even appear multi-coated, so I'd guess there is a huge profit margin on Canon branded filters. (Have you ever bought a car and been offered a $300 "sealing and protection", inside and out"? That's similar... The dealers and sales people know folks are especually vulnerable suckers when they just spent a lot of money on a new "baby" and want to "protect" it from some unknown risk. For about $20 you can get a can of Scotchguard for fabrics, bottle of Armorall for plastics and rubber, some leather cleaner/moisturizer, and a good carnuba wax for the paintwork... then in a few hours do a much better job "protecting" the car yourself.)
Of course, you can buy other brands besides Canon, but any filter is going to stop some light passing through to the lens and camera, or is going to modify and effect that light in some way. It might be very little under ideal conditions, or a lot in worst case. Quality, multi-coated filters are the least likely to do harm. Cheap, single or uncoated filters are the worst.
A filter cannot replace a lens hood. When using a filter on your lens it becomes even more important to also use a lens hood to prevent flare issues or the filter from getting broken. Plus a hood virtually never can do any harm to an image, instead nearly always improves it and physically protects the lens far better than some thin piece of glass.
If it gives you some false sense of security to drop $50 or $100 or more on a quality filter to "protect" your lens, and that gets you out shooting with it rather than sitting at home worrying about it... I say go for it, get the filter.
If you do like me and get the "protective" filter, but leave it in your camera bag most of the time... by all means slap it on there in dust storms, rainstorms and similar. But take other sensible precautions, too. These cameras and lenses are not waterproof!
There really is no way to prove that "a filter saved my lens". You'd have to buy a 100 lenses and 100 filters and do drop tests from different heights and onto different surfaces, to see if on average the lenses with the filters fared any better. Now repeat that for every lens made and with different types of filters. A plastic lens hood will deflect and absorb a most bumps. A metal-framed filter threaded into a lens will transmit any hard knock against it right through to the lens. A filter can easly get jammed onto the lens' threads. Broken glass can be driven into the front element of the lens. Over the years, I've seen some lenses ruined by broken filters, though when lens hoods are used that's unlikely.
It's easy to test for image quality effects of filters. Just shoot some test shots with and without a filter on the lens. Shoot "tough light" situations and see how many filters will cause veiling flare or ghost flare, lower contrast, less color saturation. With digital, compare the file sizes of identical shots made with and without a filter... the filtered shot will be smaller, due to some loss of fine image quality "data". It might be so little loss as to be meaningless. Or in other situations it might ruin the shot.
There are times and places that a filter helps a shot. A circular polarizer can helps deepend the blue of the sky and make white clouds "pop" in a scenic shot. A CPL also helps control reflections, not just what we notice the most off glass and water, but also on overcast days the reflection on foliage, so a CPL can improve saturation and contrast. It also can reduce reflections off skin in portraits, and is helpful if the subject wears eyeglasses. A haze or UV filter can help with clarity over longer distances, through a lot of atmosphere. A Neutral Density filter can allow you to use a combination of aperture and shutter speed that you might not be able to otherwise. A Graduated ND can help balance the sky with the foreground, in a scenic shot.
Back in the days of film, a lot of it was overly sensitive to UV light. So many experienced photographers were in the habit of using a UV filter. Other folks saw that and misinterpreted that the filter was serving as some mythical form of protection. Sales people in camera stores and filter manufacturers certainly did all they could to promote and encourage this, and continue to do so today. Though commonly used UV filters are unnecessary now, on digital cameras (which already have built-in UV filtration).