Displaying a preview is a concerted effort of the application and the OS. If there is no preview shown, that may be because that information is not available in the file, or that the OS cannot handle this information.

I would guess that the Illustrator files do not have the embedded PDF preview and that this is the reason for not displaying a preview. Bridge normally displays a preview for Adobe related files regardless of this.
(BTW: as a matter of security, I prefer to get the extension shown, so that files like 123.jpg.exe can be detected more easily. In addition, files with the same name and different extensions like 123.png and 123.jpg are easier to spot. That is unrelated to Adobe)