My theory is that graffiti is tied to the feeling of lack of agency in one's life. Everyone wants to "make their mark on the world". Some of us get to do that with an interesting career, building a family, getting involved in the community. If you feel excluded from all that, like those things are beyond your reach, you might resort to things like graffiti. IMO it's something that says "I exist, and I can change things around me" for those who don't have a better way to do that.

Based on that we "fix" the problem by making sure that everyone has a chance to make a fulfilling life for themselves. Better & freer education; Healthcare; cost of living & wage support. Etc.