It is intended that “Select box” modes not working for shortcut?
That is confusing, i would rate is as bug.
I would find it nice if for example “Intersect mode” would be working for shortcut too,
not only via button.
I might not understand what you mean, though if I do then
shortcut for box select is b.
If you use w, then you can press it again to toggle to next select mode and continue until you get to the select mode you want.
If i press “b” for box select, the status bar gives no hint for modes or actual mode, nor pressing w is changing something or changing the mode icon in the tool settings bar.
I cant find a keymap for select box mode in the preferences.