The Lost Lowdown

1. It's against the rules.

2. Widmore is Ben's constant. Killing him would be killing himself.

3. It's possible that with the time traveling that's been happening, Ben killing Widmore could create some sort of paradox. Therefore, it may be physically impossible for Ben to kill Widmore.

Any more?

I like the constant one, but I don't really see it happening. It would make sense though, if when Ben was younger and maybe widmore was his mentor or something that Ben would choose him as a constant.