Face it, government rarely does something first or best except when one government wants to eradicate another.
In other areas: The transistor was invented by the research arm of a government-granted monopoly; nuclear technology was pioneered by a government weapons project; the double helix was discovered at a publicly-funded university; we're talking to each other over a network created as a department of defense program; much of the field of artificial intelligence was developed under the department of defense.
The U.S. government linked the pacific and atlantic oceans through the panama canal; the Army Corps of Engineers made the southwest habitable; the Army Corps of Engineers built and maintains the locks that makes the Mississippi easily navigable.
The 20th century is a triumph of the American model: government policy-making and funding/subsidization combined with implementation by independent public or private entities.
(1) The transistor/monopoly theory make no sense. The US government never granted AT&T a monopoly but broke it up in 1982 when they discovered it was a monopoly.
(2) I don't think the residents of New Orleans would agree that Army Corps of Engineers should be a model for anything.
I'm sure there are some truly great non-military US government accomplishments but I just can't think of any...
http://en.wikipedia.org/wiki/U.S._Army_Corps_of_Engineers_ci...
Many people theorize, and I believe correctly, that it was entirely an aggressive posturing war between the US and USSR. We could just drop a nuke from space, with no launch to detect, so no way to retaliate in time - no mutually assured destruction, which was the only real defense either party had.
Don't get me wrong - I'm generally very liberal by US standards, and I think the Government should do a LOT more to "promote the general welfare". I just think that money doesn't care how you spend it, and governments can't set the kinds of goals that the OP proposes. Other than ending diseases, I suppose.