So, you see, that's the "vengeance" from the title -- it's not Simon going after McClane for killing his brother two movies ago (he didn't give a shit about that), it's McClane taking his revenge on Simon for ruining his life. Also, this scene takes place on Christmas, McClane's preferred date for killing bad guys, according to the previous installments.
However, according to the DVD commentary from screenwriter Jonathan Hensleigh, the studio felt that this ended the character of John McClane on a bit of a bad note. McClane has killed a lot of dudes over the years, but it's always in self-defense or to prevent them from getting away. In this case, Simon already got away. This would be the first time McClane went out of his way to coldly murder someone, and the studio felt they couldn't allow it.
Because, you know, that would have ruined the franchise.
20th Century Fox
Yes, rocket launching vigilante McClane. Nothing could be worse.