I did the experiment for my science fair and I found out that an ounce of ice with sugar on it melts in 2:30 min. While salt melted ice in 1:15 min.
Anti-freeze uses the same thing to help the water in your engine from freezing.
There were several scholars thousands of years ago debating about why the weight of a fish bowl filled with water does not change when you put a goldfish into the bowl. They argued about the reason for weeks. Finally they brought their problem to the king. The king considered it and said. I understand your arguments but I question your premise. Bring me a filled fish bowl and a scale. When they put a fish in it, of course, the weight increased.
The salt and sugar argument is the same. Many people think salt works better and you want an explanation for why. The premise is wrong. Salt is not better than sugar at melting ice. It's used on roads because it's cheaper than sugar.
Read about it here: antoine.frostburg.edu