These days nobody is going to shocked if they saw your braces, though you might get a few funny stares and comments. However, walking around with the braces showing does have a somewhat negative stereotype associated with it:
Braces are also only comfortable when you wear them with proper brace trousers. These are cut with a higher rise and fish mouth back:
The waist also has to be a bit looser than with belt trousers. When you go back to belt trousers you notice that they are more constricting around the waist. Clip ons damage the trousers and should be avoided at all cost. You can add brace buttons to belt trousers but it is often uncomfortable. As this diagram illustrates (from Flusser), brace trousers also help to hide a stout waistline:
They also straighten out the leg line and make the wearer look taller, as already mentioned. So there are numerous advantages to brace trousers. These days brace trousers can usually only be custom made, and most wearers show them off as an old world curiosity clipped on to their belt trousers.