In real world it is not the restrictions that save lives, it is people following them. If people ignore restrictions it doesn't matter whether they were or were not tightened.

Actually, if people were sane we would not need restrictions. Everybody would wash their hands, avoid touching their face, wear their mask properly (ie. not faking wearing the mask) and avoid physical contact with other people unless necessary. And all research suggests that would be enough to deal with the virus.

The fact is that Christmas in almost every country resulted in mass movement of people that just have to go and meet their families. And it doesn't matter for what reason it happened, it is just a fact.

So, regardless of whether there were or were not tightened restrictions, there is going to be an inevitable increase in cases.