Why don't poor people deserve to be a counterweight to government?
The poor have no leverage, and realistically, no one is going to give that to them.
We're not talking about an idealistic re-working of civic values, but the natural tension that already exists between private interests and the public sector.
One need only look to antitrust law to see why letting any single locus of control grow unchecked can wreak havoc on a market/economy -- I think we should appreciate the few checks & balances we have left, lest this notion of naive idealistic equality allows them to slip away unchallenged.
If anyone here wants to argue that because the poor can't effectively fight government then nobody should be allowed to 'because otherwise it isn't fair', then please go ahead. But that's the logic of plucking out everyone's right eye because one person suffered an eye injury. If your idea of fairness is reducing everyone to the lowest common denominator, I want no part of it.
It is quite easy to retard the success (or fill in the blank with legal defense, assets, education, IQ) of a group or individual. However bringing that success (or whatever) to another group is an entirely different sort of challenge, a very difficult one. There are rarely shortcuts and the most commonly suggested solutions often involve infringing on the rights of others. People don't realize this and in the quest of solving social problems with government intervention they end up creating even larger ones. Like you said, it results in pandering to the lowest common denominator. You see this very visibly with policies like "No Child Left Behind", but this sentiment tends to run rampant in leftist schools of thought.