I would save my money. Filters don't protect the lens from falls; only splashes and dust / particles.
It depends where you go to shoot. You'll find that the overwhelming majority of professional photographers leave a UV filter (or similar) on every lens they own. Something they don't mind wiping down with their shirt. Something that can be quickly replaced for under $100. Something that experience has shown them to be a very smart default position.
Run a series of tests with a clean, unscratched good quality UV filter. Filter on/filter off. You'll be very hard pressed to see any difference in your files. Wear your protection!
Filters have saved lenses from damage on multiple occasions for me. A bump against the filter thread on a lens without a hood can damage the thread more easily than you might imagine. I've bent and trashed filters then been able to unscrew them and been relieved to find the filter thread undamaged. The filter rim took the hit. For this reason I only use the slim filters on my ultra-wides. (vignetting)
Front filters are not always practical or possible such as on the 300mm f/2.8is. However, Canon knows that photographers will need to wipe these down. The front glass on the 300 is in fact relatively inexpensive plain glass, replacable by Canon for a price, but a very small percentage of the cost of a new front element.