People calling each other at new years was a thing in the before times when texting was non-existent, expensive or not widespread. People would call each other usually on land lines and caused a lot of stress to the network. It could take hours to get through. When mobile phones became a thing, people tried to be trendy and call from a party, leading to total collapse of the local cell network.

Later when texting became the norm, it would also be easily overloaded and texts could take a while to get through. These days since everything goes through the internet, I wouldn’t expect there to be any issues. The internet can handle sudden increases much better.