At least where I live, recipes can't be copyrighted because the discussion about who invented a certain dish would be way too complicated. Personally I think, when there's a tried and tested way of doing things that's the best way a restaurant can do it because customers expect a certain standard to be met when they go to a restaurant. So naturally, that's when a carbonara should not have tomatoes unless the menu specifies what has been modified or 'upgraded' (which often is not an upgrade with a good classic, imo).
But what people do at home, does not bother me one bit. If you like carbonara with tomatoes, go ahead. I will keep what I think about that to myself.
A good example of this is the Gratin Dauphinois recipe I posted, the traditional way to make Dauphinois is with just cream and no cheese. Yet almost every restaurant does add cheese these days, because this modification is so common that customers expect it these days. Personally, I love it both with and without cheese and use both on different occasions. However, if I claim to make a traditional Dauphinois, I will not add cheese. That's why I wrote it was my own version.