Yes. If you can't have both systems available at the same time and location you need to call in to have your account transferred. This requires you to answer some questions about the account such as what games do you own and when did you buy them. Then they take a few days to get around to unlocking your account. It's awful and easily the most user hostile of the modern gaming platforms' stores.
I don't understand why they do it this way. Buying a game on any other platform feels so much nicer, because I know if my console dies I can just log in and re-download. I assume it's something about piracy, but it does feel hostile towards regular users.
A plausible financial incentive for them would be rent-seeking: they might be afraid they lose money on the balance if you only have to buy the game once. Doing it this way they have a shot at getting money from you again for the same game when new consoles come out.
It actually made piracy easier. At least in the 3ds, all you need to do is add some id of the game to a file in the 3ds and it will be like if you purchased it.
Is there any info on whether this was a problem with not having Nintendo IDs linked to the shop on original Wii systems? On my Wii U, I had to create a Nintendo ID to use the shop, so presumably that follows me now. I could see the process you describe as their interim solution before they started linking accounts to the shop, but I don't know whether that's true.
