This would be unworkable
The papers would have to notify everyone about every story, and there would have to be sufficient time for the subject to object and then for the paper to appeal to a higher office for a final judgement.
And this would have to be for everyone mentioned and all in time for the morning delivery or it becomes old news.
If you want to prevent papers abusing their power then you have to have severe penalties for those that carry out the abuse.
However, we already have a situation where if you suffer a loss due to libel you can seek the redress of that loss.
So, say a person known as "M" is videoed having a leather themed orgy with 5 prostitutes, say. A paper then publishes that and maybe embellishes it a little to sell copy.
"M" then complains about the loss of privacy and that many of the embellishments are untrue and harmful.
It goes to court and there are a number of possible "hurts" suffered by "M", which may include damage to reputation, damage to character, loss of marriage, loss of job.
The judge would normally look at the damages that are caused by this and put a financial cost on them for damages purposes, however it is unreasonable to expect a court to find the paper liable for any breakup of marriage as if the whoremongering never happened then any reasonable wifey would accept this, and if it did happen then it is unreasonable to punish a paper for simply reporting the truth.
Personally I am amazed that Max received anything from the courts other than being told to go away and grow up, but there you go.