Though I don't understand your point about being offline. If you are using the current primary / secondary console, then you can't play on secondary console unless you are online, right?
I could have explained better. My docked Switch is set as secondary console, which forces online checks. That's fine because I never take it outside. My Switch Lite is set as primary console, which means it (used to be) able to play any downloaded games, no questions asked – if the connectivity check fails, it will just warn you that your cloud save status couldn't be verified.
Say I have a virtual game card of Suika Game loaded in my docked Switch. I now need to leave home, so I close the game and bring my Switch Lite with me which has Suika Game downloaded. During lunch at work, I open my Switch Lite and start up the game. That used to be fine, but now there's instead a prompt to move the virtual game card from my docked Switch at home to this one, which I can't do because I don't have internet at work. I forgot my digital copy of Suika Game at home even though it's downloaded on the console I'm holding.
This is a hypothetical example, and sorry for the wall of text, but it's a needlessly complicated system that is a net negative for the user.
Unfortunately it doesn't work like that. With this setting on, your primary console can now be locked out of games if you're caught offline and without the virtual card. That wasn't possible before.