You have the right to choose a PROFESSION but whether you can become a PROFESSIONAL is not something you deserve without working on it.
If you consider a politician is a PROFESSION, then go for it. But don't expect others will buy the criteria you set. People have the right to choose their leaders or politicians no matter what educational background they may have. If you want to exclude certain group of people from the political structure you try to propose, I am sure your system is hard to sell.