But at the same time, I think it's been shown the the size of a galaxy almost always reflects the size of its central black hole... that is, the influence of the central black hole seems to be way, way bigger than what you would expect from the black hole's gravity alone.
That doesn't follow. A galaxy is not like a star system that orbits a single massive object in a single plane. Objects orbit the center of mass of the galaxy, which is made of of an enormous mass of stars and clouds of dust and gas.
For example, the central molecular zone (CMZ) is an asymmetrical roughly spherical region, about 1600-1900 light years in diameter, that contains about 60 million solar masses of gas and dust alone, not counting the stars in that region.
That's 15 times heavier than the central black hole, or put another way, the black hole is less than 6% of its mass. By contrast, the Sun is more than 99% of the mass in the solar system - the planets are rounding errors by comparison. With the central black hole, it's the other way around.
And that CMZ gas is only about 5% of the gas in the galaxy. There's over 26,000 light years between us and the black hole, and every star and gas cloud in that enormous volume exerts a gravitational influence on us.
Zooming out a bit further, the galactic bulge is on the order of 15 billion solar masses, with a roughly spherical radius of about 6500 light years. The central black hole is less than 0.03% of that mass. If you want to imagine us and other stars in the spiral arms as orbiting a single central object, that bulge would be a better choice. But as I said, there's still another 23,000 light years between us and that bulge, filled with stars whose gravitational influence we feel.
If anything, causation is likely to work the other way around, in that larger galaxies have larger central black holes because they have denser central regions.
The questions that exist are more around how the central black hole affects galaxy formation, a sort of which came first question.
> If anything, causation is likely to work the other way around, in that larger galaxies have larger central black holes because they have denser central regions.
That contradicts the recent observations which show supermassive black holes were present as early as 700 million years after the Big Bang. That's just impossibly little time for supermassive black holes to have formed if they were just the result of matter in the central part of a galaxy to have "fallen" into the presumably smaller black hole you had in the beginning (presumably, because if you assume the black hole was already big to start with, then you must accept that the amount of matter in the center of the galaxy is a consequence of that black hole being there, not the other way around), which I believe is the theory you're proposing as more likely.
An excellent reply, far better than my idle musings warranted, however a point was missed. At some point in solar system formation the mass of the not quite yet a sun was only 6% of the mass of the entire system. At some very early point I assume the distribution of mass in the proto solar dust cloud would be the same as the distribution of mass in the galaxy.
I hesitate to reinforce my idea because really, it is ill informed musings on how solar system formation is coalescing gas and dust clouds and would galaxy sized objects eventually coalesce into the same proportion of objects. ill-informed because it turns out we can look into the past and see what newer galaxies look like.
> the mass of the not quite yet a sun was only 6% of the mass of the entire system.
That seems like an arbitrary division of the mass of the system. More than 99% of the mass of the system was going to become a star, so on what basis are you identifying a small subset of that as being significant? Gravity involves the net effect of the forces between every particle in a system.
> At some very early point I assume the distribution of mass in the proto solar dust cloud would be the same as the distribution of mass in the galaxy. [...] would galaxy sized objects eventually coalesce into the same proportion of objects.
No and no, because of the inverse square law. Galaxies don't look like large solar systems because they're much bigger. The Sun has a big effect on all the planets in the solar system, but it doesn't have much of an effect on Alpha or Proxima Centauri, even though that's our nearest neighbor.
