The United States Constitution designates specific powers of that national government, and it was thought that because of those powers being specifically enumerated, that a Bill of Rights wouldn't be necessary, as quite obviously all such other rights would be reserved to the people, because the powers not delegated to the United States by the Constitution, are therefore those powers so reserved to the people.
In point of fact, governments, especially national governments, have a very strong tendency to relentlessly increase their power over time, because those governments will invariably test their power against the people, time and time again; whereas people, and especially those people that are not well placed, or are lacking in the beneficial accouterments of customary power such as position, money, and heredity, are susceptible towards being subservient to the very government, which was created to be of benefit to them in the first place.
The importance of the Bill of Rights is demonstrated by Supreme Court decision after Supreme Court decision, when so dealing with and interpreting the first Ten Amendments to that Constitution, clearly indicative that the Constitution, without the Bill of Rights, would as practiced by this national government, be a world in which the people's voice, freedom, liberty, and civil protections would be considerably less and the citizen's powers would therefore essentially be in the strong hands of those making governmental policies.
Another important reason why the Bill or Rights was added to the Constitution is that governmental institutions have a very strong tendency not to want to debate the law in any sort of open and democratic format, but rather those powers would prefer to make or to interpret law in a manner in which the people are made to be obedient to that government, and therefore for the people, not to have the fundamental right to question or to circumvent what the government believes to be their domain.
At least with a written Bill of Rights, the people are able to call upon those rights, whenever it is felt that their rights are being trampled upon or violated, in which this sort of healthy pushback, often precludes that government from obtaining even more control over the people or of being able to place even more weight upon the back of that population. Unfortunately, governments don't often wish to cede ground when it comes to their accumulation of more power, so that, even when the people are successful in maintaining their rights, the government is often relentless in trying to take what they can back from them, piece by piece, so that, the people ultimately still must bend to the government, even though, such bending, is clearly not part and parcel of their Bill of Rights.
America prides itself on being the land of the free, but this is truly a chimera, for a free people, should not be deliberately targeted so as to be stopped and frisked for simply walking the streets, of which this mindset of "us v. them" is reflected in the over 10 million yearly arrests in America; of a country which has not a single person or judge that thoroughly knows, understands, and can comprehend every single law of this land, but rather, far too often, treats its own citizens in a manner which seems to stipulate, that might makes right, and further that the people are not equal, and that they certainly do not have any unalienable rights, but only such rights as this government so determines that they have, at the discretion of that government, held back only by the inconvenience of that Bill of Rights.