There are probably different types of inefficiencies that relate to, among other things, having to be more accountable for spending tax payer dollars. If $LARGE_CORPORATION chooses a given vendor for a major software system, the losing vendors may piss and moan but there's really nothing they can do about it in general. If it's a government agency, there will likely be formal challenges requiring lots of paperwork and effort.
But, for the most part, I agree with you. Big organizations can do things smaller ones can't but that size comes with a lot of overhead. I'm often surprised not that large organizations are inefficient, but that they can get anything done at all.
I challenge anyone who says government is inefficient to find me a single large corporation that ISN'T inefficient.
It has nothing to do with government and everything to do with size.