I would say consistency is one of the most important things you can have in a fictional world. While you give up the ability to write whatever drama you want, the consistency is what gives that drama its relevance.
I agree, drama needs consistency to be relevant - but consistency also needs drama! Otherwise you'd end up with a perfectly logical, bone dry protocol of events, not a entertainment product. Of course, in a perfect world we we would always get both, but it's really,
really hard to make something entertaining (for a broad audience) and long-time consistent. That's why there are so few examples of it. In reality there has to be compromise somewhere, although I'd agree that the balance is all too often tipped toward the entertainment side.
Fighting consistency-entropy is hard but it is necessary! For the good of nerdom!
You could almost define a nerd as someone who values consistency higher than the average consumer. If you do, that would be a never ending "fight" (because of a changing average). I think at the end you can do more for your enjoyment of media by accepting the necessity of compromise