The people who wrote the Constitution apparently didn't think so.
The people who wrote the Constitution were not the ones who wrote the Bill of Rights.
The righting of the Constitution took place over an incredibly grueling summer that George Washington presided over. They were closed door sessions, and they argued with each other relentlessly on how the Constitution should be written.
It was any wonder that the Framers were able to do what they did.
When James Madison sent a summary of the Constitution to Thomas Jefferson in Paris, who was serving as a minister-at-large to France, he was appalled that the Framers had not included a Bill of Rights to serve as protections against the federal government.
So this argument in the public over whether or not the Constitution as it was written was brought up. This was the fight between the Federalists, who were proponents of adopting the Constitution, and the Anti-Federalists, who were against the adoption of the Constitution because it didn't provide enough protections for individual freedoms and liberties, and is the source of the Federalist Papers.
Finally, a compromise was struck between the Federalists and the Anti-Federalists. The Anti-Federalists would agree to endorse the Constitution if the Federalists agreed to adopt a Bill of Rights afterward. The deal was struck and the Constitution was adopted
without the Bill of Rights.
Once the first Congress was in session, James Madison, a Representative, took to the task of drafting the Bill of Rights. He took admissions of proposed rights to include in this from anyone, and all these he whittled down to about 80. Then they were down to 18. Then 12. Then 10.
Once Madison drafted the Bill of Rights, Congress debated it for some time but then agreed to pass it as per the agreement to adopt the Constitution.
My source for this?
iTunes - Podcasts - The Thomas Jefferson Hour by Clay Jenkinson