This seems different and a bit lacking in detail (although I don't dispute that it could be useful). How exactly does one choose m and C? And what are the conditions under which it would reduce to the James-Stein / Bulmannn / BLUP model?
1. If there are no ratings, Bayesian average is close to overall mean, and
2. If there are many ratings (how many depends on how big the site is), C and m do not affect the result much.
You probably can do a little better if you have a lot of data and ability to run A/B tests, but for vast majority of cases pseudocounts work just fine.
It would be interesting though to have people try to guess suitable values of m and C and then see how close their MSEs get to the James-Stein MSE. I suspect that some people's guesses would be meaningfully off target.
So the test would be to randomly split users into test and control, show ranking based on Bayesian averaging to control, show ranking based on James-Stein or some other method to test, measure some metric of user happiness (a different hard problem, click rate on top titles?), then do the comparison.