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.