Why aren't solenoid/electromagnet windings insulated?

It is insulated. Have you ever noticed that sometimes solenoids are made from copper wire that seems distinctly non copper coloured?

This is called enamelled copper wire, and it available in a whole range of colours.

The insulation is just a very thin coating of polyurethane, polyamide or polyester. It shouldn't be confused with vitreous enamel, which is glass. The good thing about it is that you can easily remove the insulation by rubbing hot solder on the wire.

The wire is actually insulated. Most solenoids I've seen are wrapped with magnet wire or something similar. The wire is coated in a small amount of an insulating material. To create an electrical connection, you have to scrape off (or otherwise remove) this coating.

This insulation is thin and more windings are placed on the solenoid core than would fit with other insulations, it is also usually fairly indifferent to high temps. The goal is a high magnetic field in a small space. Often called magnet wire, transformer wire....