28mm tires start becoming inadequate when the surface is either not hard-packed or is wet. 32mm tires (aside from very aggressive knobby CX tires) don't do much more either in those cases.
I ride 42-45mm tires. Great for say rural pea gravel parking lots that 30mm-class tires will just sink into and leave you walking. Also for how bad paved roads are, I'd much rather ride 42mm tires at 40PSI---than 28mm tires at 80PSI. Although if the surface is so loose as to want a bigger tire than a 45mm, you probably want a fatbike anyway.