I see the icon thing with jwm, though Icewm and I am sure the others make use of the internal icon spec, which if I recall jwm does not, but rather depends on an icon that shares the same name as the app or process.
The problem we will run into when renaming icons to match the process name is that it takes our freedom away from being able to name extensions as we please and use the extension name for the name of the icon so different extensions do not have file conflicts. We would have to use the icon name "opera.png" for every opera extension, and since we have several versions, that will result in file conflicts. And I would rather stick to the principle of having no file conflicts.
And, yes, using Icewm alleviates this issue. :-)
Thanks for the testing and feedback, and I wished there was a way to support jwm without compromising on more basic principles.