We've talked about exactly this internally (it looks like the bug filed on it is from 2 years ago already ), and I still think it's a good idea! Just a matter of finding the time to get it implemented.
Maybe the custom card and icon could each be an (optionally) transparent image, overlaid on the existing frames.
(Though custom animation would be neat too if you could write multiple images. Or: specify CERTAIN numbered frames to put your overlay on, rather than on all of them.)
Just adding my vote for this feature; and since it hasn't be mentioned yet (exactly) this would also be really useful for productivity type apps. e.g.
Calendar app that shows upcoming meetings
Todo app that shows the top prioritised tasks
Basically working like a widget in Android. In my own case I would like to highlight an 'article of the day', the titles of which should easily fit in that space.
This does seem like a neat idea. I could see games design their cards to show high scores, or other bookmark-like data that remain in the carousel to invite players back into the game. Sort of like a notification, without actually being an intrusive notification.