In the generally accepted classification of gates, there is no dividing onto synchronous and asynchronous. I came up with this classification a couple of years ago, analysing the principles of operation of Contax shutters, developed a hundred years ago for the Contax II and Contax III. I described this in more detail in my article published here at this link (will open in the new tab): https://kosmofoto.com/2021/04/the-curious-case-of-the-contax-shutter/. If you wish, you can understand my classification and why I decided to classify shutters in this way.
And in a nutshell, as a result of this article, synchronous shutters are more reliable, more stable in their work. It’s just that the development of photographic shutters went in the direction of asynchronous designs.