Let's keep it on track.
"One of the commonly disputed topics in society and politics is whether a nation should seek to..."
Do you mean the government or the populace? In countries where the government is elected by a minority there is likely to be huge differences in opinion.
"level the playing field" - definitely! You can't have one rule for the privileged and another for the not so privileged. That includes mandating equality - Martin Luther King, among many martyrs was all for that.
If the UK law on accounting had been level with US laws, the Lehmann Brothers debacle would not have been as wide spread, they would have had to file for bankruptcy earlier with less repercussions on the market.
"redistribute resources" - In a healthy society this would normally be achieved by trade. Unfortunately there are no healthy societies these days so the government (at whatever level is seen to be best) must be prepared and qualified to assist in this.
"mandate equality" - definitely!
The first and foremost duty of any nation is to look after its citizens. Either through defense, education, resource management (energy, water and air) and health care. If it does not fulfill this then why do we need nations, why not let the utility sharks and the bankers get on with it?
In non democratic countries you don't expect any of the above, but most eastern European countries had most of that before the fall of the Berlin Wall. Democracy won't guarantee that the will of the people is carried out as we can see in most democratic counties these days.
I am not knocking America in this so no-one needs to get insulted, this is the sad reality of most of today's greed orientated societies.
Whoever said all men were created equal was talking through his naval. This has never been the case, and never will be. For a start, almost half the "men" are born as women, where is the equality there? I won't even start on the not so able bodied, or the different ethic and religious origins, or whatever.
To sum it up, it would be nice to say YES to all three, and then have it work!

Chris