But in actuality just the opposite is the case.
When there's more poverty everywhere, people have an innate natural tendency to withdraw internally, and shut all that poverty out which surrounds them. Mentally they go into defense mode, and feel less willing to share what they have.
When poverty is everywhere surrounding you, you just have a feeling like the entire situation is hopeless and no amount of money is really going to make any difference. As well as a fear that if you do not hold onto your own saved money, there's a remote possibility out there that you could end up one of those people.
Look in countries like Mexico. The rates of altruism are very low. (Compare Bill Gates and Warren Buffet who donated almost all of their wealth to charity, versus Mexican billionaire Carlos Slim who told one inquiring reporter "Don't expect me to go around being like some sort of Santa Claus." )
The greater the problem is, the less people will care about it.
There's also the psychological phenomena of donor fatigue, and feeling overwhelmed. That's why when you see charities on TV soliciting your money to help hungry children in Africa they will typically try to focus on just one child. When the viewer sees that, subconsciously they will feel that their donation can make a difference. Paradoxically, if they showed big crowds of hungry children, there would be a tendency for the viewer to feel emotionally overwhelmed, like the problem is so big their donation is unlikely to make much of a difference to the problem.