Jim, I was installing windows—the real ones, not the operating system. Had that been the case, I still wouldn't be here…
Actually, your definition is very good. You directly or indirectly mentioned every function of a primer: surface sealing, increasing adhesion, corrosion resistance, increasing hide (true color), surface leveling, and protection of the substrate from the top coatings if they are incompatible with it (such as many lacquers and styrene.)
Except in specialized systems (such as Alclad) primers are most often flat because this promotes better bond to the top coat. In scale modeling, the most important functions of a primer are probably detection of surface imperfections and surface adhesion. With Alclad, the purpose of the primer is to protect the plastic surface and possibly to provide a very smooth surface and a certain amount of color enhancement.
Other than for specialty coatings like Alclad, you can use any flat paint (compatible with styrene) as a primer, provided that it adheres well to the plastic or resin of your kit. My favorite is Tamiya light grey acrylic.
Some people have reported problems with Alclad's primer. I suspect that these are due to use of incompatible solvents, but I haven't investigated the problem. However, this brings up an important point: whatever you use as a primer, if you thin it, be certain that the solvent you use as a thinner is completely compatible with the paint.