I know that's like a formulaic crack, but the last time I was at the DMV, I did wait like 2.5 hours ... because there were a huge number of people being served by a small number of people.
That's what efficiency looks like. Each transaction took a small amount of time, the clerks processed each one efficiently and had little downtime between them. Each clerk was maximally utilized, and the DMV was fully utilized all day.
A DMV where you could walk into at any time and a clerk was available to help you immediately would be incredibly inefficient: it would have too many clerks who were being paid to stand there not working. Convenient, yes, efficient, no.
I think it is very much a case-by-case basis, depending on a number of factors. Factors include, but are not limited to, what part of what government, purpose/mission, funding, incentives, and local culture.
Yes, one can find examples of incompetence and inefficiency if one looks, but one can find the opposite as well. I think a blanket attitude of government == inefficient incompetence is an unhelpful one, and a major part of how you get DMVs that deserve the purgatory comparison.
That's what efficiency looks like. Each transaction took a small amount of time, the clerks processed each one efficiently and had little downtime between them. Each clerk was maximally utilized, and the DMV was fully utilized all day.
A DMV where you could walk into at any time and a clerk was available to help you immediately would be incredibly inefficient: it would have too many clerks who were being paid to stand there not working. Convenient, yes, efficient, no.