I do think this is a fascinating question. One that rather perks me up and has me asking "Yes? So why don't people think this way?"
Can you be on the left and also believe that the state really does have to be much more lean and much more efficient?
Why is it that it's people like us, people defined as being upon the right, who are always going on about the efficiency of the State in doing things? That it actually ought to be efficient at the things that it does?
Surely, if you were (in this left right political sense) of the left, if you wanted to argue for greater State involvement, you would be arguing even more strongly than we do that the State must be lean and efficient in what it does? You might well think that it should be doing more things, but your insistence upon lean and meanness should be even greater than ours, no? You do, after all, want it to do more things from those limited resources available and you're also trying to argue that it's a great way to get things done.
But of course this isn't the way it generally works out. Those arguing in favour of State action rarely are those arguing that we should examine the efficiency with which the State does things.
I suspect a large part of this is that what is generally referred to as "the left" isn't actually anything either left or right. It's just the producer interest speaking, one of the more conservative forces known to man.
But there's also a chink in there, room for the argument that it is we classical liberals who are truly of the left, as we have been for centuries. Yes, absolutely, there are some things which must be done and things which can only be done by government: therefore government must do those things which must be and can only be done by government. But then end aim of all of this is to provide the average person, the working man, that Clapham Omnibus rider, with the best deal possible. Which means that the State must be efficient so as to extract as little as possible from the pockets of the populace to fund what it must do: leaving as much as possible to fructify and benefit us all.
Our concern for efficiency is exactly and precisely because we're on the side of the people, not the producers like the conservatives of the so-called left.