All my lenses have b&w filters and I don't see degradation. When I'm slipping lenses in and out of bags the front gets dirty with dust, fingerprints. I have no worry wiping them off with a tshirt or a cloth. They have saved my lenses from liquids before and some impacts. If you baby your gear sure but as a pro I don't have time to be worrying about my front element.
I have decent multicoated filters on all of my lenses too... I try to baby my gear, but S___ happens.... I placed an order last week to B+H and it included a 77mm UV filter to replace one with a big scratch down the middle. I have no idea how I scratched it or what I was doing when it happened... but I am a lot happier buying a new filter than sending a lens across international boundaries for a new front element.....
I also have some polarizing filters.... One is a "Henry's special" and the other is a Sigma Multicoated.... there is an immediately visible difference between the two.. If you think cheap filters are bad idea for UV and clear filters, then you are really going to hate a cheap polarizing filter.
HINT: When buying "specialty filters", such as polarizing, ND, infa-red, etc... buy them for your biggest lens size, and then get some step-up rings for the smaller lenses.