We kind of do though, or at least their scope.
If you are hacked then games is not an issue, outside of playing online which has been covered. If they make some kind of subscription service a la PSN+'s free games or the many equivalents I am sure the names of said games will be plastered everywhere and onto lists.
I guess you will not have any access to a cloud server for game save storage... I can knock that out in about 5 minutes once a basic homebrew set of tools appears, 10 if you want a nice versioning one so you can roll back your save to all sorts of points, maybe 30 if you have a particularly awful home router and want some fancy online wizardry done as well. Given most people will probably be happy with a simple "copy to SD/USB" type setup though that might all be almost redundant.
They might make an application that grants access online video streaming service and tie it to their services. Almost anything there I expect homebrew to be able to replicate, or if you prefer
https://kodi.wiki/view/Category:All_add-ons and if the android ports hurry up and get sorted then... yeah.
We do have an example of local video play being blocked from banned 360s (you might see people talking about being flagged but not banned), though it was mainly the DVD hacked stuff and that did not grant control over the system.
If they make a web browser and it is even vaguely usable then I doubt they will proxy it through their servers, and if for some bizarre reason they try to prevent banned people from using it then the checks will probably be overwritten in a few hours.
Are there any other classes of application we see or are likely to see that will cause even the slightest bit of aggravation to those wanting them then I can't think of them.