One issue with the Bayesian average is that with a straightforward implementation it will end up pulling really bad manga too close to the mean. It wouldn't be a problem normally but in rating you want bad stuff at the bottom, not near the middle. In systems where the real average isn't the expected average (real average is actually almost 8 but the implicit expected average is 5.5) low ratings get pulled too high, when ideally predominantly low ratings would be weighted more.
This does work if you want to encourage people to read the low manga more and get it to its actual rating more quickly, but I think it's bad user experience, especially paired with the seeming lack of relation between the histogram and the final rating.
I don't know where that fudge factor would end up or to what manga it would apply, but it might be best to increase the weight of low ratings for manga with lower numbers of reviews. The problem with this is that a manga with only 1 star ratings would have their rating increased with each new 1 star review. Maybe scaling the distribution from the real Bayesian to the expected average before calculating would work and then mapping back, but maybe it would do nothing at all. I might do some MATLAB to figure it out later.
It may be intended, but sorting manga by rating is still based on the mean rather than the Bayesian average.
EDIT: The mapping trick does not work. As I feared, it doesn't do anything in the end.