There are certain advantages to suspenders that belts don't have, and certain advantages to belts that suspenders don't have. In the nineteenth and early twentieth centuries, formal and semi-formal clothing was mostly worn by men of means, either the hereditary wealthy or the bourgeoisie, joined by what we might call the managerial class (lawyers, corporate managers, etc.). The wealthy, in other words. All of these men wore bespoke clothing, meaning clothing that was designed and constructed specifically for their bodies. Tailored clothes, as you might imagine, fit really really well. But, your pants still might have a tendency to fall down, especially since bespoke trousers tend to be on the looser side, for comfort. Therefore, each pair of bespoke trousers would come with a set of buttons inside the waistband, designed to have a special piece of underwear, called braces or suspenders, hooked into them. By hooking them over the shoulder, the pants can keep their looser fit while still staying exactly where the wearer wanted them. Generally, men who wore braces kept their jackets on all day, so the braces wouldn't show.

For factory-made, generic-sized pants this is less practical, so the belt is the preferred solution. It's also an easier tailoring job to sew loops at regular intervals than to add the tabs and buttons for braces. As more men (professionals like salesmen and middle managers) began to wear suits after WWII, suits began to increasingly be sold off-the-rack, made in factories. These clothes adopted the easier and cheaper expedient of using a belt. But tabs for suspenders are still available for bespoke and high-end made-to-measure and off-the-rack clothes, and many men who shop at that price range still wear them. It offers superior fit and prevents you from having to re-tuck your shirt and hike your pants, but you also have to keep your jacket on all day, something that is less and less common in this casual era.