Why would anyone use a prior so strong that when presented with data, they would be unable to learn from it. In that case, if your prior is that strong, did you really have any intention of attempting to learn from new data?
I think that the concept of a prior deserves more attention as the strength of your current beliefs in the face of new evidence.
Presumably, if you have a subjective prior, you brought some "prior" experience or knowledge to the problem.... so philosphically, where does the original prior come from, and if it comes from your experience, is it really a prior, or have you actually reasoned your way to a posterior without even realizing it? Perhaps more time should actually be spent justifying your prior if you are going to bring a subjective prior to the problem. If you have good reasons and a lot of quality evidence, then the prior should receive a lot of weight.... deciding how much weight and how strongly you believe in your prior is a tough question.
I think that any time you create a prior without objective evidence able to support it, you have the potential to bias your results. But then again, if you truly believe in your subjective prior, do you really care about the potential to "bias" your results?