The Sun, all stars, galaxies, formed by ordinary matter self gravitating into a volume where it's components interact with each other. With ordinary matter that implies a confining pressure produced by gravity, and a resisting pressure from the particles interacting with each other and not being able to share the same volume.
As a "RetiredChemist", you should recognise that situation from deriving the "Ideal Gas Laws" from Newtonian dynamics of particles and Van der Waal's expression for the volume of gas molecules (as opposed to the volume occupied by the gas under NTP, STP or whatever. REmember that lecture.
The thing about normal matter is that it's particles self-interact, leading to them having a consistent distribution of particle energies. And that means a gas of normal matter has a temperature, and it will radiate some of that energy away if it's temperature is greater than the ambient (currently 2.8-odd K ; the CMB temperature). Otherwise, it will collapse in volume under the influence of gravity - as you suggest - until it's internal temperature rises to the point that it starts to radiate it's thermal energy. Yadda, yadda, normal star formation theory, and on a bigger scale the same process for galaxies.
But with dark matter particles not (or very rarely) interacting (DM)particle on (DM)particle (and little from (DM)particle on (NormalM)particle), they just pass through your volume under consideration and out the other side, only responding to the gravitational force very slowly braking them as they ascend from the gravity well and into inter-galactic space. Then they slowly descend back into the middle of the galaxy, picking up speed from the gravitational field ... and pass through the middle of the galaxy without interacting with other DM (or NormalM) particles to shoot out the other side.
According to the -CDM model, DM does clump with matter - at the galaxy or galaxy-cluster scale. But it doesn't stick to other DM as well as "NormalM" does, so it hasn't (yet) condensed into dark galaxies etc.
Re-do your "Ideal gas law" calculations with a much smaller Van der Waals volume and much weaker electrostatic reaction between gas particles, and you too will reproduce the slowness of clustering. You could manage this when you were an undergraduate ; you can do it now.