Yeah that's not how it works, you lose weight and fat gradually goes from all different areas.
Working out causes muscles to grow and get stronger, so bodybuilders can target specific areas, but fat doesn't get worked when you work out, fat burns due to needing extra calories to survive, you don't choose where the fat comes from. For example people have chubby fingers, they run for a few months and lose their chubby fingers, they didn't go finger exercises to lose them.
The weight will gradually go and the belly fat will eventually follow. It all depends on where your body is decided to get the extra energy from.
Except that it did work for me cause that's exactly what I did years ago. Granted I was never really fat, just a bit too much around the belly. After a few months of intense sit-ups, not only did my muscles down there grow but the fat began to substantially decrease. Maybe this would not work if you're too fat, I don't know, I can only speak of my experience.
Though after a while I simply stopped these daily intense sit-ups cause I realized I was running after something that demanded too much effort and could never be fully obtained. I was looking great down there sure, but at the price of having to do this for ever cause it's not like one needs to do that for a time then one can stop and the fat never comes back. So now I got a bit of fat down there again, not too much, but it's not the near perfect abs that I used to flaunt back in the day. These days I simply don't care anymore.