Most digital cameras are not susceptible to UV light, so would it be better for me to remove the UV filter to get the best image quality or should I leave it on for lens protection?
It's generally accepted that UV filter don't really do much to affect the video/photos, good or bad, but like you say most people use them to protect the actual lens.
Jonathan's right. The UV filter is just cheap insurance for your lens. I keep them on my regular camera lenses and I've had many instances where something has splashed or hit my lens and the filter took the abuse.