Constitution protects us from dictators and tyrants. Allowing a president to remain in the office indefinitely based on public opinion, which can be manipulated, would be too risky. Being a politician is a service to your country, not a career.
Not only should they not be removed, but Congressional term limits should be added, beyond which they are not allowed to participate in govt at all, not as lobbyists, consultants, etc. They are done and are in the private sector.
They also should not get benefits for life either, that is a burden that society should not have to bear.