Firstly they are, like socks, underwear and almost always hidden by your outer clothes. This gives you far more flexibility to wear something colourful, luxurious, or just a bit silly (like braces in your old school colours). On the rare occasions when they are made visible, they add a pleasing splash of colour, either glimpsed beneath an open jacket, or properly exposed at that point in an evening where jackets are removed and ties loosened.
Image from Albert Thurston
A second, perhaps more important, reason is that braces will make your trousers look so much better. The only way a belt can keep your trousers up is either by resting on your hips, which is not a good look for a suit, or by being tight enough to grip the body above the hips, which pulls in the waist of the trousers and is also a pretty terrible look. By contrast, trousers worn with braces hang neatly off the shoulders, meaning they retain their intended shape, and can fit snugly at whichever point on the body you choose to wear them, without needing to be pulled tight or constantly adjusted. Braces also avoid the tendency of trousers worn with belts to sag slightly at the front, especially on men with anything less than a washboard stomach, and help prevent shirts from becoming untucked.
Ideally, braces should not be elastic, but in either silk or boxcloth, and attached via leather tabs to buttons inside the waistband of your trousers. Some of the best known are made by Albert Thurston, which are available in the UK from Woods of Shropshire amongst many other places.