First rule of time travel: You can look, you can touch, but you can’t change anything. No bug killing, no foot print leaving, hell, you don’t even want people in the past to see you. Any changes you make will effect everything to come after that point. It’s the biggest rule of time travel, the famous one. Time doesn’t want to be changed, either. If it senses something mucking it up, it tries to expel it.
So what happens when you take a man, strip him of his memories, leave his desire to survive, and dump him back in time? He fights his way forward, changing what has come before on instinct. And time? Time just keep pushing him forward to minimize the damage.
How is Bruce Wayne a weapon aimed at the 21st century? Because at the rate he’s going he’ll have completely altered history on the way to getting there.