Why did the Constitution not include qualifications for members of Congress other than the ones stated below?
Qualifications: The legal qualifications for our congressional representatives are spelled out in the Constitution. To run for senator, you must be at least 30 years old, live in the state you plan to represent, and have been a U.S. citizen for at least nine years before being elected. Members of the House of Representatives must be at least 25 years old, live in the state they represent, and have been a U.S. citizen for at least seven years before being elected.
The Framers of the Constitution did not include any other qualifications for membership in Congress because they wanted American politics and government to be as open as possible.
The Framers included the qualifications that are in the Constitution for specific reasons. They did not feel people below the specified ages would have the experience and wisdom needed to govern. They wanted people in Congress to have lived in the United States long enough to have a real commitment to the country and long enough to understand the nature of the United States. The same rationale applies to the state residency requirements.
But outside of those criteria, they wanted a government that would be open to all. They did not want to impose property qualifications on Congress because they wanted the government to be more democratic than that. The same logic applies for why they did not impose educational requirements. They did not impose religious qualifications (and in fact strictly forbade them) because they wanted American government to be open to people of all religions.
In short, the Framers wanted a government that would be, as much as possible, open to all sorts of people. Therefore, they did not impose many limitations on who could serve in the Congress.