There have been a lot of good, interesting answers here. There seems to be a consensus, though, that I honestly have trouble understanding, and that is that Doctor Who NOT really changing or ever taking itself seriously is a good thing. That kind of begs the question, doesn't it, as if I asked, "Why won't it change?" to which the answer is, "Why should it?" Well, clearly that's not an answer, but an indication that one finds the question irrelevant or not worth engaging with. But that is precisely my question - why do fans believe the idea of the show taking itself more seriously (not TOO seriously, thank-you, just MORE seriously), is a bad idea? Why the resistance to the idea? By all accounts, when the show DOES do that, they occasionally create a masterpiece.
Look - Doctor Who fans are not unintelligent fans. They are, in some ways, more perceptive and honest about what they see than many Star Trek fans, fans of a show, arguably, that has much more serious intentions. And Doctor Who fans are aware of when they see something truly brilliant and exceptional - Earthshock, Caves of Androzani, The Doctor Dances, Blink, Midnight - so, clearly, these fans are not without critical faculties. They give credit where credit is due. They recognize that some episodes are clearly far and above other episodes in quality.
And yet, and yet - Robot of Sherwood gets 5-star reviews all over the internet. "Brilliant!" they say. "Witty!" "Absolutely engaging!" they say. 5 Stars! 5 Stars! 5 Stars!
But wait a minute - if Robot of Sherwood is 5 stars, what is City of Death, or The Romans? If Into the Dalek is 5 Stars, then what is Genesis of the Daleks? Isn't there a curve here? How can we give Into the Dalek and Robot of Sherwood 5-Star reviews, when we know the show is capable of City of Death and Genesis of the Daleks?
So, here's what I see happening: Doctor Who fans tend to be extremely perceptive and generous when the show creates brilliance, but they CHOOSE to put aside their critical faculties whenever an episode doesn't hit those incredible highs. It's an intellectual decision, I think. It's like trying to find the good bits in your annoying brother-in-law. They know that the show rarely hits those highs, so they choose to pretend that the rest of the time, it's hitting very close to those highs anyway. (Robot of Sherwood, 5 Stars? Really? Really?) How else can we explain 4 and 5-star reviews on episodes that come NOWHERE CLOSE to being as good as Doctor Who can be? This is part of what I mean when I say that the show doesn't take itself seriously enough, most of the time. The fans don't seem to, either. They seem perfectly happy when a show that has created Blink and Midnight and Girl in the Fireplace can so very often not even bother getting out of bed in the morning.
But can't we expect and hope for episodes at least closer in quality to episodes like those classics more often? Shouldn't we hold the show to those high standards, the way, say, Deep Space Nine fans tended to? (There's a fanbase that expected great things from its show, and had no trouble calling a turkey a turkey, let me tell you.) Why the laissez-faire attitude? Why is good enough good enough?