This feels like it should make sense, but I think misses the forest for the trees. It's an example what I'd refer to as first-order thinking, or looking only at the immediate situation.
We need to be striving for higher order thinking. That is, we need to be looking at follow-on effects, which I'll analogize to looking at the second and later derivatives of a function, or looking at other elements in an interconnected feedback system (in the control theory sense).
Is not asking whether the graffiti was intended to intimidate somebody considering the follow-on effects?
Sort of. How about an after school "chess club" where the kids who attend get free dinner, and there are a variety of educational activities to choose from in addition to chess? How about a free camp where you bus all the kids out to the nearest wilderness every weekend to learn archery and play sports, and the kids who attend don't have to worry about not having food and shelter for two days out of the week?
> What if the tagger chooses not to go?
Not all of them have to go. You don't have to solve the entire problem at the same time. And if it doesn't work, you keep trying things until something sticks.
The key point is that you need to be willing to spend the resources keeping kids out of jail that you would spend keeping them in jail.
These sorts of clubs exist in some places, such as in my school [0]. They include everything from tutoring to other academic activities to free meals to summer programs.
Only if we're punishing them under the same circumstances, which I don't agree is necessarily the case. I think we should punish someone who marks graffiti in order to mark gang territory or intimidate others more harshly than someone who does it as a prank.