Board Thread:The Flash discussions/@comment-9346948-20181205013242/@comment-24152851-20181207024241

Doesn't that defeat the whole point though? They punish him for messing with the timeline but now he's just free to roam around and screw with the timeline further. It would just be easier to erase him from existence.

In fact on Legends, Nate explicitly said what Eobard was running from was "the non-existence catching up to him"