Why use software that requires installation if there's software that doesn't?
[Ignoring the actual time needed to use the application and create the icon. I can guess that a native application will further reduce this time.]
* As I wrote earlier, because of browser limitations, there are very few web applications geared towards icon editing/image editing.
- You generally own the license to the installed software in perpetuity. Your application source art will always be readable.
- It will integrate better with your desktop user experience. Printing, drag-and-drop, copy/paste of complex data, input devices (wacom tablets), etc.