You see, I wouldn't have a problem if Booster had never tried to change the past and had a mission of just preserving the timeline from others trying to change it. Because doing things like killing Hitler or Joker could potentially have really bad consequences.
Say Booster does go back and kills the Joker. Oh look, now the world has been destroyed because the JLA needed Oracle, but Barbara never became Oracle. She's either retired from heroing or prowling the rooftops of Gotham (Hopefully as Batwoman,not -girl by then). Or perhaps some one the Joker would have killed gets into a drunk driving accident and 9-year-old Tim Drake is killed in the crash. Or perhaps one of Booster's own ancestors ends up marrying someone Harley Quinn would have killed intead of their 'proper' spouse, and Michael Carter never exists, so now we've got a paradox on our hands.
Time Travel is never as simple as 'Kill bad person as a kid, the world becomes a better place'.