If everyone has a college degree, then no one has a college degree.
I understand what you are saying but there is a huge demand for vocational education programs that are NOT taught in high schools or typical 4 year college programs.
I know the president of the local community college here in NH. It was formerly called the NH Vocational Technical College.
Their program in automotive body work is sponsored by several local automotive dealerships. Every person coming out of the program has a job. Some of the local car dealers pay for kids to go through the program.
In addition, they are trying to get an airplane mechanic program. An air traffic controller program. Even a airplane pilot program. Another program they are trying to develop is welding.
So, no I do not think community college should be free for ALL programs. We certainly do not need more Gender Studies graduates. We need more DIRTY JOBS graduates.