Have Labour just made a big mistake on the benefits cap?

This is one of my favourite exchanges from Yes Prime Minister:

Sir Humphrey Appleby: [discussing how to stop the PM's anti-smoking legislation] I think the crucial argument is that we are living in a free country and we *must* be free to make our own decisions. After all, government shouldn't be a nursemaid, we don't want the nanny state.
Sir Frank Gordon: Oh, that's very good.
Sir Ian Whitworth: Excellent.
Sir Humphrey Appleby: The only problem is that that is also the argument for legalising the sale of marijuana, heroin, cocaine, arsenic and gelignite.

I wonder if Liam Byrne may come to wish he had had an Appleby around to provide a counter-argument when coming up with Labour's latest approach to the benefits cap. He writes in todays Telegraph, in a piece entitled "The same benefits cap won't fit London and Yorkshire":

But the problem with the Government’s proposal – as presented – is that “one cap fits all” won’t work.

Most of the benefits paid under the cap are for housing. But these are far higher in places like London than in other areas. While all that £500 a week might get you in central London is a one-bedroom apartment, in Rotherham, Yorkshire it would get you a six-bedroom house. How can a “one-size-fits-all” cap be fair to working people in both London and Rotherham? 

Perhaps if he had have done the exchange could have gone something like this:

Sir Humphrey Appleby: I think the crucial argument is that a "one-size-fits-all" cap cannot simultaneously be fair to working people in both London and Rotherham.
Liam Byrne: Oh, that's very good.
Sir Humphrey Appleby: The only problem is that that is also the argument for agreeing to regional pay bargaining and even regionally varied benefits. Which the unions and the grass roots of your party will never accept.

Surely that is now Byrne's and Labour's problem. The coalition has been pushing the idea of regional pay bargaining for a while now which has thus far been responded to by protest from Labour MPs. How can they now credibly fight that when they have made pretty much the exact same argument the government make in favour of it in the context of a benefits cap? I can hear Paxman sneering now. If there is such a difference in the cost of living between different parts of the country then how can you possibly argue against regional bargaining? Do you even understand your own policy Mr Byrne?

I expect they'll have an argument against this but I fear it will end up as convoluted as their approach to the cuts and will be far too easy for their political opponents to shoot down as muddled and incoherent.

How much longer can Labour keep dithering around like this before Miliband's position becomes untenable?