Nothing, it still works as usual. It will probably display that your account is still linked, since it wont be allowed to contact Nintendo anyway.
Some very specific games hides LAN-multiplayer behind linked accounts, but there are workarounds for that.
What if I don't unlink my account from the banned Switch and login to the new Switch with said account, will I be able to download and play my legally bought games from eShop?
Yes. The bans issued by Nintendo involving CFW are usually console-only (online play, updated and CDN access), the account is still on good standing. I'm not sure if a repeat offender would be forgiven again, tho.
Some people are paranoid enough to believe their account will be banned. Others have purchases made on that account they would rather not risk losing.
The console bound games past losses is a fair enough excuse. It's great to see nowadays we can recommend OP to unlink and redownload the games on another console.
Hope everything goes well and Nintendo proceed with what OP are going for.
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realtimesave:
@SylverReZ NIntendo pretty much has to release a new console by next year in order to keep making moneys imo+1 -
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realtimesave:
they need to have a strong line up on the launch titles too. I think they should move metroid prime 4 to the next console because by now it has been quite a while and there's no release date scheduled yet
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