You are wrong about one thing. It is the people who should actively seek solutions to poverty, crime and war. By giving that power to politicians, you ensure that there will, in fact, be more laws passed and no solutions found. People need to stand up and take the responsibility back from the government and quit relying on that government for their every need and whim.
How do you propose people to end war, crime, and poverty. I'm especially interested in hearing how you end war. What control do people have over the military?
So what exactly happens in the absence of government? Or a Representative Democracy? Would abusive, rich, powerful individuals just disappear?
Depends on the newly established system. If you consider the resource based economy, then cybernated systems will handle the "government" part which is mainly concerned with distributing resources. Corruption will be made irrelevant by the system. Right now, its profitable to be corrupt. But in a resource based economy, there is no incentive to be corrupt and not possible to "attain power".
"The auto lobby (carmakers, insurance companies, aaa etc) do their best to ensure that there's insufficient public transit/public transit of insufficient quality, forcing people to buy cars to get around..."
Care to give specifics on how these industries you just named actively ensure there isn't sufficient public transportation?
"In the United States, automobile and tire manufacturers conspired to close down the US streetcar system in the Great American streetcar scandal." http://en.wikipedia.org/wiki/Tram#Demise_in_the_US
New systems generate new problems.