Presumably because they are trying to be a "startup", they are copying the business style of startups. It's easy to look back afterwards and say "that was a complete waste", but it's possible that at the time it was seen as justified. It's easy to say we'll just take the good aspects of startups and the good aspects of government agencies and reject the bad", but it's not always apparent what is the good and bad in each, as they are both fundamentally systems whose ultimate behavior is emergent from all their aspects. It's very easy to accidentally break something useful by tweaking or removing something that appears completely unrelated in systems like that.
That said, I think the more interesting question is should we be trying to emulate a startup in government, given that the vast majority of startups fail? In that light, it should be absolutely no surprise that 18F is failing. It was the likely outcome.
One thing that bothers me about government websites is the boosterism of whoever is in office. Secretary of State websites are particularly bad in this regard. Usually you go to the SoS website to do something related to licensing, like the DMV. Both Illinois and California have had headshots of the Secretary of State displayed prominently in the header. It is labeled/named something long winded like "Secretary of State Joe Blow's Department of Motor Vehicles Website". Is it on a .com or a .gov or a .(state).us domain for any given state? The generic "(welcome and platform) message from the Secretary of State" is often front and center.
Really, who the Secretary of State is is so secondary to the actual services being provided, all this does is serve to tell everyone who is responsible for this crap website.
If there was consistent branding, and that branding was strong and recognizable, citizens would be better served. You wanna toot your horn, put some metrics up like the last 6 months of turn-around time on license approval, website and phone service response time, help topics researched, costs to provide the services, etc, and show me how access to state services are improving over time, which is the SoS's actual job. Government agencies usually have weak branding because it gets upset based on term lengths (except for services like the IRS, which has pretty consistent branding and methodologies).
This isn't just a website problem either - the DMV in Illinois is really the Jesse White center based on the amount of branding and pictures you run into there.