I agree that poverty and homelessness will never really be eradicated.  Even with basic incomes schemes, there will always be a percentage of people at the lower end who will qualify as poor.

In theory we can stop global warming.  In reality, in practice, we almost certainly cannot.

Cancers can potentially be cured one day.  People will likely always get it for the reasons you mentioned (and just bad "luck"), but there may be a day when medicine can cure one when they are afflicted like we do with bacterial infections.