Maybe this should be in the Wish List, instead of FAQ.
The only way I can think of in the selection Properties Palette, is through Metrics - solid state, if it shows a volume its solid.
As a workaround instead of messing with the menu. Turn on the Solid/Surface toolbar. Then you have a simple visual guide without opening menus. Or possibly better, create a new toolbar, and put just the two solid / surface buttons on it. then there is only two icons to look at instead of all five. One just has to remember the object is the button which is greyed out, not active.