Here are a few additional considerations.
Lens hoods are great, but relying on them solely for your lens protection means you are stuck with:
A - having full sets of filters for each lens with a different attachment size
B - not using square or rectangular filters such as graduated ND filters (personally I don’t do this anyway, I just deal with it in post)
C - using those cheap rubber lens hoods that aren’t optimized for your lens - for instance if you use a standardized set of filters with step-up rings which negates the opportunity to use the the manufacturers lens hood if the attachment size is not the same as the native size of the lens
I only own 5 lenses, 3 are 77mm filter size. One is 62mm - a macro lens. One is 67mm - a 70-200mm f4 zoom that is lighter, sharper, and less expensive than the f2.8 version (for me all of those are positives in favor of the f4 lens). So to rely solely on the lens hood for protection would require me to carry three sets of ND and polar filters - more bulk, more weight, and greater expense (all negatives in my opinion).
High quality filters have not degraded image quality in my experience. I do use clear protective filters. I carry one set of 77mm ND and polar filters plus a spare polar and a spare clear along with step-up rings. When I can’t use the original lens hood I use an old dark slide to shield the lens from flare. I also agree with several posts that cleaning a filter is easier than cleaning the front element of many lenses. Also, I have scratched at least one protective filter in the last 2 years - it could just as well have been the front element of my lens.
So for me, there is no perfect answer to this filter dilemma but, for me, the best compromise is what I’ve outlined in the previous paragraph. So you’ve got filter lovers, filter haters, and compromisers - take your pick and move forward. But I’d rather not rely solely on a lens hood to protect the front element of the lens.