I'm with Flying. Press shutters have limited top speeds -- Copal Press, 1/125; Ilex Universal, 1/100 and they don't come very close to that; Alphax, ditto -- so force one to use small apertures at high noon. This isn't always what the shot wants. And the limited top speed often limits how flash can be used out-of-doors. For flash 1/400 is preferable to 1/125.
That said, a used press shutter often costs quite a lot less than the equivalent cock-and-shoot.