Blur object background
I'd like to see a blur option where objects behind an object appear blurred such as in the attachment. This is something that, I believe, can be achieved in CSS so it would be good to have the ability to use such an effect in Illustrator.
Olivier Robert commented
This should be upvoted a lot. This effect is now supported in all major browser using CSS (see backdrop-filter) and is an effect broadly used in today's modern design.
This concept could be broaden to 'Allow separate transparency masks for each appearance item'. This will give what you request and more, without breaking existing paradigm.