This whole question is a mistaken premise. There are spherical (or at least nearly spherical) galaxies! They fall into two basic categories - those elliptical galaxies that are pseudo-spherical in shape and the much smaller, so-called "dwarf spheroidal galaxies" that are found associated with our own Galaxy and other large galaxies in the "Local Group".
Of course when you look at a galaxy on the sky it is just a two dimensional projection of the true distribution, but one can still deduce (approximate) sphericity from the surface brightness distribution and large line of sight velocity distribution for many ellipticals and dwarf spheroidals.
Dwarf spheroidal galaxies may actually be the most common type of galaxy in the universe.
These galaxies are roughly spherical because the stars move in orbits with quite random orientations, many on almost radial (highly eccentric) orbits with no strongly preferred axes. The velocity dispersion is usually much bigger than any rotation signature.
There is an excellent answer to a related question at Why the galaxies form 2D planes (or spiral-like) instead of 3D balls (or spherical-like)?
Pretty pictures:
UK Schmidt picture of the Sculptor dwarf spheroidal galaxy (credit: David Malin, AAO)
The E0 elliptical galaxy M89 (credit Sloan Digitized Sky Survey).
Details: I have found a couple of papers that put some more flesh onto the argument that many elliptical galaxies are close-to spherical. These papers are by Rodriquez & Padilla (2013) and Weijmans et al. (2014). Both of these papers look at the distribution of apparent ellipticities of galaxies in the "Galaxy Zoo" and the Sloan Digitized Sky Surveys respectively. Then, with a statistical model and with various assumptions (including that galaxies are randomly oriented), they invert this distribution to obtain the distribution of true ellipticity $\epsilon = 1- B/A$ and an oblate/prolate parameter $\gamma = C/A$, where the three axes of the ellipsoid are $A\geq B \geq C$. i.e. It is impossible to say whether a circular looking individual galaxy seen in projection is spherical, but you can say something about the distribution of 3D shapes if you have a large sample.
Rodriguez & Padilla conclude that the mean value of $\epsilon$ is 0.12 with a dispersion of about 0.1 (see picture below), whilst $\gamma$ has a mean of 0.58 with a broader (Gaussian) dispersion of 0.16, covering the whole range from zero to 1. Given that $C/A$ must be less than $B/A$ by definition, this means many ellipticals must be very close to spherical (you cannot say anything is exactly spherical), though the "average elliptical" galaxy is of course not.
This picture shows the observed distribution of 2D ellipticities for a large sample of spiral and elliptical galaxies. The lines are what you would predict to observe from the 3D shape distributions found in the paper.
This picture from Rodriguez and Padilla show the deduced true distributions of $\epsilon$
and $\gamma$. The solid red line represents ellipticals. Means of the distributions are shown with vertical lines. Note how the dotted line for spirals has a much smaller $\gamma$ value - because they are flattened.
Weijmans et al. (2014) perform similar analyses, but they split their elliptical sample into those that have evidence for significant systematic rotation and those that don't. As you might expect, the rotating ones look more flattened and "oblate". The slow-rotating ones can also be modelled as oblate galaxies, though are more likely to be "tri-axial". The slow rotators have an average $\epsilon$ of about 0.15 and average $\gamma$ of about 0.6 (in good agreement with Rodriguez & Padilla), but the samples are much smaller.
