Seems the game requires a constant internet connection in order to unlock things due to how the Krypt and Towers of Time mode were designed. Also seems even having a constant internet connection isn't enough since its rumored you also need to have an active sub with Xbox Gold, PS+, or Nintendo Online as well.
Story mode and regular/classic Towers mode are not affected for unlocks.
https://www.resetera.com/threads/mor...-krypt.111786/
https://www.gonintendo.com/stories/3...ar-unlocks-tow
https://gamerant.com/mortal-kombat-1...net-gear-mode/