The problem with Solaris, Windows, and other desktop workstations at the time was that the second (and even third) mouse buttons were required for many workflows, especially in applications---i.e. a lot of functionality was only available from the right-click menu or via the middle mouse button. This introduced a lot of unnecessary complexity to computer use, especially for new users, because of low visibility and discoverability.
Even today, Mac hardware never has a visible 2nd mouse/trackpad button. Sure, you can click a trackpad with 2 fingers or tap on the right side of a mouse to get a context menu, but keeping the buttons invisible forced these shortcuts to remain just that, and not an essential requirement to get the job done. Windows apps today follow this rule as well -- never make right-clicking the only way to execute a particular function.