I simply prefer the look of natural light. I do understand correct usage of flash, and the look is quite different to me. There is a large, and growing, number of wedding photographers who avoid flash unless there's absolutely no way to shoot with available light. Jeff Ascough is a noteable example.I don't understand the resistance to flash, I have been shooting wedding for years and as long as you understand the the correct ususage of flash and how it interacts with the film, the results can be quite pleasing.
Not sure which "other problems" you're referring to?At least it works for the type of weddings I do, I would rather work with a flash that with the other problems associated with not using it.