This was studied many years ago.
Not only do galaxies have to hold together, but there also has to be enough matter to hold it tightly enough to spin at the speed it turns. (Imagine swinging an object on a string around your head, the faster it spins, the more force you have to apply.)
(Note that galaxies don't actually rotate like a single solid object would. Instead different stars orbit at different angular speeds depending on their positions. However that's not an issue for this question, because we can still calculate the galaxy's total mass and mass distribution, that's needed to produce the rotation we observe.)
It turns out that not only the central black hole isn't nearly big enough, but even the black hole plus the mass of all the stars, planets, gas clouds that we can see, still isn't nearly enough.
So we know that unless there is some aspect of the laws of nature we don't know about, there must be a lot more mass in most galaxies than we can see. Both of those possibilities have to be considered.
We don't think that new features in the laws of nature are the real answer. There is other evidence that suggests laws like gravity operate on galactic (and even apparently cosmic) scales much like we think they do. Too many experiments over the decades would have given different results, if gravity worked much differently at galactic and larger scales. So we don't think that's the answer.
So the answer is that galaxies include a lot more matter that somehow, we aren't able to directly detect, but we are very sure must be there. We can't even detect any extra matter on the scale needed, in our own home galaxy, the Milky Way. We call this unseen matter "Dark Matter" because it's unseen (dark) to our detectors, and we have some ideas what it could be, but we are still trying to prove what it is and directly detect it.
The evidence for this also famously includes studies of colliding and non colliding galaxies. We can study the images to determine where mass seems to be, and where gravity seems to be acting. For example, gravity distorts distant light ("gravitational lensing") and we can study where the centre of that distortion occurs. In non-colliding galaxies the results suggest that gravity effects occur where the mass is - they are centred in the same location. But in colliding or recently collided galaxies, gravity effects are found to be displaced to a different location than the visible mass distribution would suggest. If gravity itself acted differently than we believe, or there was a flaw in our workings, we would expect to see an effect in all galaxies not just colliding ones. But in fact we only see such effects in galaxies whose mass is being disturbed,or was recently disturbed, and this supports the belief that there is a much more massive and larger distribution of unseen matter, whose distribution/shape is usually symmetrically around the galaxy but during a collision is distorted, causing the galaxy's overall mass distribution to change, much more than the movement of its visible stars would suggest.
So the central black hole in galaxies isn't what holds them together. It might have the mass of millions of stars, but the Milky Way contains hundreds of billions of stars - about fifty thousand times more - and a huge amount of dark matter too, which we know is there in a form that our instruments can't yet "see". Some estimates suggest that the mass of this dark matter could be huge - almost 10 times the mass of the visible stars and matter (90% of the galaxy's total mass) and extending out more than 10 times as far as the visible stars of the galaxy - taking the galaxy's total mass to maybe as much as 1.5 trillion suns.
The central black hole is impressive, and a feature of the galaxy, but it's completely insignificant in terms of holding the galaxy together. If it suddenly vanished, some stars near the middle would change their orbits, but the galaxy as a whole would be almost totally unaffected. You'd almost not notice it.
What holds galaxies together is the immensely greater mass of their dark matter halo (as it's called), together with their visible stars and objects generally, for almost every galaxy we have studied.