Forgive my utter ignorance but, what if black holes are not "holes" but solid spheres of massive density? There you may have your dark matter to boot.
“Based on a statistical analysis of 740 of the brightest supernovas discovered as of 2014, and the fact that none of them appear to be magnified or brightened by hidden black hole "gravitational lenses," the researchers concluded that primordial black holes can make up no more than about 40 percent of the dark matter in the universe. Primordial black holes could only have been created within the first milliseconds of the Big Bang as regions of the universe with a concentrated mass tens or hundreds of times that of the sun collapsed into objects a hundred kilometers across.”
“An as-yet unpublished reanalysis by the same team using an updated list of 1,048 supernovas cuts the limit in half, to a maximum of about 23 percent, further slamming the door on the dark matter-black hole proposal.”
I don’t think you meant dense though, I think you meant mass, because that’s sort of how your post seems to be phrased. The answer then is that it is a minute fraction of the mass of the galaxy. Sag A* is about 4 million solar masses, and the Milky Way has 250 billion stars, many of which are far more massive than Sol. Even ignoring other objects like stellar remnants and nebulae, the mass of the central black hole is negligable on the scale of the whole galaxy.
We know that the rotational velocity of a stellar object is proportional to the mass inside its orbit and inversely proportional to its distance from the center.
From measuring the velocities of stars in other galaxies, we find that the stars distant from the core are orbiting much faster than we'd expect them to. The velocity as you go out from the center should drop off quickly; it doesn't.
Therefore we hypothesize that there is a lot more matter at the outer reaches of a galaxy than what we're seeing.
So... you need not just more mass, but mass that isn't clumpy; mass that is mostly at the outer reaches of a galaxy and not the center.
A massive black hole at the center just doesn't cut it.
As to it being a source of dark matter, the idea that black holes and other compact objects are dark matter is encapsulated in the MACHO (MAssive Compact Halo Object) theory. It is extremely unlikely to be correct, because observations largely rule this out. Black holes warp spacetime around them and result in detectable phenomena as a result of gravitational lensing. It would appear that such lensing is not common enough to allow for black holes in sufficient quantity to explain dark matter.