Maybe CR thought that leaving town would be too suspicious.
He could not have predicted how much of a big news story this turn out to be. I believe when he committed the murder (especially if we are speculating this is not his first time at the rodeo), he honestly thought he'd just wipe off his hands, get back to his normal life as usual, and people would barely talk about Mollie.
Instead, pretty much immediately, she became national news, FBI swarming in, huge manhunt, and everyone in their small town concerned and talking about it. If someone during this time decided to simply up and leave their life, that would certainly point a spotlight at them if there wasn't one before.