Leaniyas daati the whole thing sounds like a shtus (if no yidden are learning then the world goes back to tohu vovohu) but it has it’s mekoros so there you go.
There are in fact many mekoros to go either way. There were many great Tzadikim who, in fact, didn’t learn on Nittel, some even on both the 25th of Dec. and the 6th of Jan. As far as your Tohu Vovohu problem is concerned, when it is nittel here in NY it is the next morning in Hong Kong or Australia. In fact if you figure it out that way, Shabbos in fact is on the globe for a full 48 hours.