Offering money to drop out of high school would cause the drop out rate to increase further. Besides, I get the feeling that most high school drop outs aren't really looking for work. This is a hard problem to solve.
The money would be unconditional, not in exchange for dropping out of high school. You may as well say that soup kitchens are offering soup to drop out of high school and are causing the drop out rate to increase further.
It has some advantages over more traditional welfare systems. For instance it could be implemented with far less bureaucracy and would help improve labor mobility in the middle class by decreasing the friction of changing jobs and moving to different areas with better jobs (improving labor mobility would benefit the economy at large).
18 is probably too old. We want the child support handout to be separated from the parent as early as possible. Giving 12 year olds their own income is probably better than either welfare queens or fertility police.
