Not a scientist but I assume galaxies are flat because they are not ONE whole full object (mass) like planets and stars, but a collection of them.

A spiral galaxy consists of a disk embedded in a spheroidal halo. The spheroidal halo consists mostly of Dark Matter (DM), and the DM makes up 90% of the mass of the Milky Way. Dynamically, it is the DM, that, ehrm, matters. And DM will always arrange itself in a ellipsoid configuration. But the visible matter can have spiral or elliptical pattern bc of conservation of angular momentum and centrifugal force we acts separately from gravity. P.s the solar system is flat too.

The rotation and the enormous mass of galaxies flattens them but there are galaxies which aren’t flat. Transcript from astrophysics for people in a hurry: “The stars of the Milky Way galaxy trace a big, flat circle. With a diameter-to-thickness ratio of one thousand to one, our galaxy is flatter than the flattest flapjacks ever made. In fact, its proportions are better represented by a crépe or a tortilla. No, the Milky Way’s disk is not a sphere, but it probably began as one. We can understand the flatness by assuming the galaxy was once a big, spherical, slowly rotating ball of collapsing gas. During the collapse, the ball spun faster and faster, just as spinning figure skaters do when they draw their arms inward to increase their rotation rate. The galaxy naturally flattened pole-to-pole while the increasing centrifugal forces in the middle prevented collapse at midplane. Yes, if the Pillsbury Doughboy were a figure skater, then fast spins would be a high-risk activity.” Excerpt From Astrophysics for People in a Hurry Neil DeGrasse Tyson This material may be protected by copyright.

Some arent tho like Jupiter or Saturn