Actually, it is not a matter of cooking "style". It is a matter of properly completing the dish or lazily not completing the dish. The chemistry and physical nature of the pasta itself demands that it be mixed with the sauce while still hot in order to properly absorb some of the sauce and become something more than it was before. When you order a cup of coffee, the server hands you a fully brewed cup. She does not hand you some ground beans and some hot water. Were she to do that, she would be handing you an incomplete dish, and there is no way that you could finish the process at the table in a way that would be as good as if the coffee had been fully brewed under controlled conditions. (However, if the server brings you a French Press with the water and coffee not yet combined, you could finish this off the right way, but you would have been given the proper tools to do so.) Same with pasta. The porous pasta and its accompanying starch is made in a specific manner to blend with the sauce to absorb it the way water mixes with the coffee grounds. Without a final mixing under heat, you cannot achieve the finished product. I suppose that a restaurant that ladles sauce on top could, if it wanted to, provide the diner with a warm bowl or a pan and heating element and allow the guest to mix the pasta and sauce together at the table. But have you ever seen that done? The other problem with the "sauce on top" error is that it almost always involves rinsing the pasta. Otherwise, the pasta would stick together in a clump by the time it got to the table since it hasn't been tossed in the sauce. The photo above of the "sauce on top" pasta certainly looks like it has been rinsed. And doing so removes the starch which is an essential element that allows that sauce and pasta to marry. While it is certainly the case that more restaurants than Tony's fail to mix the pasta with the sauce, the fact that the error gets repeated does not convert an error into a "style". For more on the subject, I recommend:
http://www.domenicacooks.com/2013/10/pasta-and-sauce/
http://www.seriouseats.com/2016/02/the-right-way-to-sauce-pasta.html
http://www.mariobatali.com/videos/saucing-pasta/
http://www.finecooking.com/articles/how-to/perfect-marriage-pasta-sauce.aspx?pg=1