The first two paragraphs are pretty amusing, but I disagree about the serious stuff. I don't think there would be any difference in the amount of political energy expended in having a weak government, but that energy would be put to even less use than it is now.
The theory Hyde outlines would involve pretty much taking a snap-shot of how things are now and preserving it as very little could change. At least when governments change they can implement the policies people voted for. Would the minimum wage have ever come in with a weak government? No, of course not. But those recent measures that Hyde goes on about being terrible were generally passed with conservative support, so those things wouldn't have changed.
Whereas the more lefty things that I'd imagine she would prefer, like NMW, need a strong majority to get passed.
I know it's a joke and I'm being a serious boring bastard, but there we go.
Strong government at least gets something done, and that something is backed by some form of mandate.
As for Ashcroft and Cameron, well, we all know that they're only getting in because Labour is so unpopular