The entire principle of giving out a general-purpose diploma is the core flaw in the question. Rather, everyone should be trained from the beginning of their schooling towards a certain set of "certifications", qualifying one for tasks or jobs of varying difficulty levels, or which have given pre-requisites.
Thus, rather than producing HS grads who are all over the map as far as skills and working capacity, and seeing a need to encourage a greater amount of self reliance generally, it may be wiser to start measuring when each student becomes "ready to work at McDonalds" versus "ready to be the assistant manager at McDonalds".
Rather than being a means to leave at-risk or learning-disabled children behind, such a system could (with the exception of legal requirements to work certain jobs) eliminate age as a factor in learning, reducing the feeling of pressure to perform and/or conform with one's nominal age-based peer group. Further, since no high school diploma would exist to signify the "end of compulsory education", follow-on courses of study could simply target themselves directly at the appropriate qualifiers, along an ever-evolving life-learning path throughout one's lifetime, without a stigma of "leaving the real world to go back to school", and hopefully without an equally outmoded sense that higher education as well need follow strict 2/4/6 year lengths for any work-practical reasons.
Given that nearly everyone entering school now will change career paths multiple times before retirement, this changed format overall may help reduce the "abandonment factor" experienced currently by seasoned workers whose fields disappear due to outsourcing/automation/other factors.
What would the impact be if high schoolers had to demonstrate the skills to start and run a small, local, service business in order to receive a diploma?