I tend to the view that poverty is being unable to meet basic needs such as housing and food. Unequal wealth distribution tends to involve inefficient allocation of capital so if there are many people of good character that are having problems making ends meet that would be an issue.
YES!
And in this case, significant wealth inequality would simply be an indicator, a signal that something is wrong in the society.
It's not a root problem in and of itself that needs to be corrected. If the *real* root problems are fixed, the inequality will likewise be corrected. To try to suppress the symptom instead of curing the disease seems a waste of effort to me, and a distraction from the real issues.
First, you have absolute poverty. I think it can be subdivided into two categories: (1) getting enough food and water to be able to survive another day (probably around $1-$2 a day); (2) getting varied and healthy food, access to the means to achieve that like a fridge, having electricity, having electric lighting, having time-saving devices like a washing machine, having Internet access and a basic computer and finally having a shelter for the weather.
We can all agree that people not having (1) is a big problem in and off it self, no matter if it is a symptom of something else. (2) is in my opinion about where everybody needs to be to be able to eliminate absolute poverty completely.
When it comes to relative poverty, or income inequality apart from absolute poverty, it is a whole different discussion. I definitely think there are a number of things that are wrong with society that end up causing gross wealth inequality. But sometimes the symptoms themselves can kill you, and in such cases one needs to treat the symptoms first before one can fix the root cause. I think that gross inequality causes absolute poverty, crime, loss of opportunity and a negative feedback loop. In other words, one of the causes of gross wealth inequality can be wealth inequality in itself.
So I do not reject that one should find the root problems in society and tackle them, I'm saying that we cannot ignore glaring inequality, simply because it causes too many problems.
Now on to the root problem. I think what we are talking about here is culture. People in general need to have a more cooperative culture. I'm not saying that healthy competition is bad, I'm just saying that if you play football (soccer) and while dribbling your opponent falls down, the right thing to do is to help him/her up, make sure they are okay and continue playing trying to win - kicking your opponent while down might help you win the competition, but it is not part of a culture that is beneficial in the long term.
Translating this to a real life situation, one can see that if someone is having problems, people having an ideal culture will try to help. But this is where most people (and NGOs and governments) fail badly - giving them a free lunch is just likely to make them dependent on you, you would actually not be helping them at all. What you need to do is educate them, teach them the skillsets they need to take themselves out of their hardship, thus creating a positive feedback loop for them. However, the further down someone is, the harder it is to teach someone the right skillsets - in these situations one needs employ the best teaching methods for teaching hard lessons: tricking them into realizing by themselves how to improve.
My point is that if one really wants to tackle the evils of the world, starting by teaching people how to resolve their misery and better their life as a means of reducing inequality is a great way to do it.