Unless you're willing to support this by some peer reviewed papers on how orbital mechanic differs between the singular system and the whole galaxy, I call boo on that.
Call what you like. The maths
is the same, and orbital mechanics remain the same over Newtonian distances and masses (relativistic physics notwithstanding), but how the two are talked about is different because of the differences in scale of both size and relative mass. The key difference is that the sun contains 99.9% of all the mass in the Sol system while Sag A* contains about 0.000003% of the mass of the Milky Way. Discrepancies in the maths caused by calculating orbits within the Sol system ignoring the gravitational effects of the rest of the galaxy are therefore negligible. Hence we talk about "the Sol system." This doesn't take peer reviewed astromechanics papers to demonstrate.
Galaxies are bound together internally by mutual gravity; bodies within a solar system are also bound together by mutual gravity. The key difference is the distribution of mass and its gravitational effects. It's why it's convenient to say that the Moon orbits the Earth - despite the combined mass of both bodies orbiting the sun; the dominant interaction in the Earth system is the mutual gravitational attraction between the two bodies.
Milky way would most certainly NOT remain spinning as a well behaved homogeneous blob of matter if Sag A* were to disappear.
That's not what I said. Be fair, and I will reciprocate. The galaxy will not fly apart with every star proceeding on a straight line. There will, of course, be disruptions to the orbits of all stars, but these will take millions of years to play out. Given the inverse square rule, not much will change, gravitationally speaking, in the outer arms. They will still happily orbit the barycentre.
Yes, it's not singlehandedly holding the whole thing together but the STRUCTURE of the galaxy very much depends on it. Sag A* is orbited by thousands of massive stars that are being born and destroyed and other black holes and together they make up the core of the galaxy, orders of magnitude more massive than the SBH itself. That lot is then orbited by hundreds of millions other stars around the centre, and those then make up an orbit mass for the arms. And so on. Like an onion made of stars. But it all still very much depends on that one pin in the middle.
We don't even know what 84% of the galaxy
is. dark matter is responsible for the outer parts of the galaxy rotating at a similar speed - more or less - to the more central regions. The distribution of matter in the galaxy is a lot more uniform than you seem to be suggesting.
There are galaxies that possibly don't have SBHs in the middle and if you look at them, although they are holding together by mutual gravitational fields, there is no structure and there most definitely is no spin. That's why we have a different name for them -globular clusters. Because that's what they are - a blob of stars. It also has a "centre of mass" but it is not orbiting it.
Globular clusters are held together by gravity - the stars are densely packed together and gravitationally bound. If they're not in orbit of a barycentre, they're falling in towards it. They're not stationary objects relative to each other.
Our solar system is the same as Milky way, btw. For example Mars is not orbiting just Sun. It's orbiting Sun, Mercury, Venus and Earth and its orbit reflects that. It's just that on smaller scale a star IS much more influential because of the disparity of masses. But the maths still works the same.
Cf. my initial point about the disparity in the mass distributions. The maths is the same; the numbers are radically different.
