I couldn't decide at first if I thought this was bad writing (because they didn't realise the story fundamentally doesn't work) or very clever writing (because they knew perfectly well the story doesn't work and used rather skillful sleight of hand to hide it). The more I think about it, the more I think it was the latter.
It seems to me that Moffatt wanted to explore the moral dilemma of a no-win scenario. There are a lot of great themes and concepts that come under that umbrella: necessary evil, the needs of the many outweigh the needs of the few, sacrifice for the greater good, sometimes the only choices you have are bad ones, etc etc -- see everything from The Wicker Man to every season of 24, to Torchwood Children of Earth. It produces great stories, but they all have one thing in common: they're not just dark, which Moffatt can do very well, they're BLEAK. Too bleak, I think, for a family show. COE explored those themes to tremendous effect, but that was Jack. The Doctor could never do what Jack did.
What Moffatt really needs is a no-win scenario that still manages to have a happy ending, but the problem with that is that it can't be done: those things cancel each other out. A true no-win inevitably involves suffering, which means it can't turn out to be all okay in the end. If it does, it wasn't a true no-win to start with.
So what do you do? Turn for inspiration to James T Kirk in the Kobayashi Maru test, and change the settings of the game, that's what.
'The Beast Below' is presented as a moral dilemma story. It does look like one, thanks to the atmosphere of hidden menace, the central conceit of 'the truth is so terrible that people would rather wipe their minds than deal with it,' Amy's reaction to the video and the Doctor being all 'oh, we should never have come here'. We're primed to expect a situation where there are No Good Choices. And when we do find out about the space whale, both Liz 10 and the Doctor himself specifically and explicitly confirm this. Liz 10's video gives her only two options: keep things the way they are, or disintegrate the ship. The Doctor tells Amy that she was trying to save him from an impossble choice: humanity or the alien. This is the Moral Dilemma: do you carry on torturing the space whale, or kill the humans? The Doctor, the cleverest man in the Universe, can only come up with one other option, another bad one: lobotomise the whale.
It looks like a no-win scenario, it walks like a no-win scenario, the Doctor -- the character we most trust to tell us the truth -- says it *is* a no-win scenario. So it must be, right?
There *are* other options, but we've been conditioned to believe they don't exist so we're not looking for them. And, just to make extra sure, we get beaten repeatedly over the head with the Great Enormous Anvil of OMG DOCTOR = SPACE WHALE DO YOU GET IT DO YOU SEE WHAT I DID THERE Y/Y? until we're too concussed to actually think about it.
The thing is, the whale isn't in agony because it's carrying the ship. The whale is in agony because they have cut open a section of its head and effectively shoved an electric cattle prod into its brain -- which is, we're told, the 'throttle,' to make it go faster. But bearing mind that a) they don't seem to be going anywhere in particular and b) the ship is completely self-sustaining and they can slow the ageing process, there's no reason at all that speed should matter. So they don't need to torture it to make it go faster. And since the Doctor's lobotomy plan proves that it can fly the ship without being in pain, they clearly don't need to torture it AT ALL.
They don't even need Amy's revelation and (actually rather risky) strategy of releasing the whale straight away. They could have just stopped cattle-prodding it and let it fly at its own speed while they worked on, you know, just as a thought, building a freakin' engine to fly the ship instead. Especially since they've got the Doctor on board -- I'm sure he could've rigged something up in half an hour with two toothpicks, an ipod and a piece of gum. Or if they did want to set the whale free -- since the TARDIS is capable of pulling a whole planet across half the galaxy, the Doctor could have towed the ship himself until the engine was running or they reached somewhere habitable.
The Moral Dilemma of 'save the whale vs save the humans' is a completely false dichotomy, because the whale's pain is not an unavoidable consequence of sustaining human life. It's something they chose to do, and could just as easily have chosen to stop doing at any time.
But I guess that wouldn't have been much of a story, would it? :-)