To paraphrase Keynes: asymptotically, all methods work.

Looking for ways to take more data is a good idea. Pretending you can always crush your uncertainty with available data is not.

Bayesian analysis is expensive? Compared to what?

You know what's more expensive? Trying something else. Bayesian analysis practically writes itself (I use Jaynes' notation). I break it out when I'm just trying to clarify my model of a situation. I find it so much easier than the sea of special case techniques and jargon in classical stat.