Near zero is being slightly overdramatic.
While I would agree I can not be absolutely certain. I have long maintained that I had one of the best offline experiences I have ever had with the 360 (DVD modded and especially JTAG, only really the PC or DS stands a chance of beating it) and if you looked at those a lot of the kids would consider them worthless following a banwave.
That said I drive everything I own into the ground and never really resell anything I use so it is not something I note terribly much. Mind you if people are prepared to sell me banned systems for a couple of drinks and shipping then I am OK with that, assuming the Switch gets some games.
Trading Pokémon, next year
Online trading maybe, offline stuff I can't see happening in any practical manner that won't be immediately figured out and bypassed.
The only thing I would care about is losing game and system updates, if they decide to ban people from updates in the future. We live an age where games are shipped unfinished with day 1 updates, or are incomplete with additional downloads required.
At least with DevMenu we can install .nsp updates manually, but that will require someone to dump them, or having a safe method of downloading them from CDN after being banned.
System updates would probably make for legal issues in various places. If you have to wait for hacked versions of system updates to hit then... welcome to hacking.
Equally I can't see a world wherein collections of updates would not be scraped and made available via less official means if it became an issue. Dox divisions doing updates/patches have been a staple of the warez scene since it became a necessary thing, though trainers and cheats also fell under it before then. Earlier I mentioned the 360 title update scene (though you could have updates transferred by any number of means, including to completely unhacked devices). If you are considering the general meh that was the 3ds scene when it comes to updates then don't.
Safe methods of dumping might be made tricky for the person doing the average hacked system install but it is nothing for someone that wants to provide said updates with the sort of hacks we have available.
Sure, it was just an example, my point is we have no idea what other kind of services nintendo might restrict in the future, it's all up to them so no one can say for sure, we also don't know what kind of stuff might become available on switch in the future that will be already restricted from banned users, it's just a warning.
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.