Let me settle this. (to a degree) Yes, dried pasta is better for dishes where you need starch water to add salt and starch. The flour that dusts fresh pasta doesn't quite do the same thing. That makes more of a slurry. You can do it, but frankly I have never had the same result when preparing dishes like cacio e pepe, carbonara, or other dishes that rely on the starch water. As far as the al dente bite, you can still get this with fresh pasta, but you need to be quick with the strainer.
With the above mentioned recipes you would never add butter or cream. They aren't part of the deal. In sauces that have extended cooking times like a Bolognese or ragu, you need oil, butter, and the fat from the meat to carry the longer cook time. Olive oil can't handle cook times beyond 30 minutes, it loses its flavor. Then it hands off to the butter and eventually the natural fat. That is what makes a complex sauce that have layers of texture/flavor.
I love fresh pasta with bolognese, ragu, or a quick pomodoro or aglio e olio. It also makes the best lasagna.