A few words come to mind when I look at some government websites: boring, skimpy, graphics light, no video content, not configured for mobile users.
You see them and they don't draw you into looking deeper for information. My first thought is, "I'll be it is going to be hard to find the information I want."
Take two examples from the same agency. There is the Colorado Office of Emergency Management which is pretty typical for what we might see on our OEM websites across the nation. Then (because I picked up via Google Search--they had relaunched their website) see the Colorado Division of Homeland Security's webpage. See the difference! I like the heavy and "upfront" presence of social media prominently displayed on the home page.
I don't want you thinking I'm the pot calling the kettle black. My own personal website at ericholdeman.com needs to be refreshed--re-skinned if you will. Same content, presented differently. I got a rough estimate and it will cost around $4K for someone who knows what they are doing to make the changes needed. So, until I save up enough pennies it will have to wait.