Democracy is about equality of rights, not equality. People are not equal in every aspect, but they should be equal in front of the law, for example.

Freedom is not absolute because your freedom stops where somebodys freedom beginns.

Hence, if you practice medicine without qualifications there is a high chance you will hurt somebody. It is not undemocratic to protect against hurting others. Hurting others is not a right.

Interesting thought exercise though.