Christianity has had such a tremendous impact on Western history that without it, the modern era would be unrecognizable. America and the nations of Europe may never have formed, being replaced instead by different nations and cultures. America has a lot of problems, many of them thanks to Christianity, but it's still my home, and using time travel as irresponsibly as that would be like using a nuclear weapon to kill the cockroaches in your house.
Furthermore, I wouldn't go back in time and kill Hitler, either. As a result of that madman's useless pogroms, boatloads of those smart Jews came over to work for us. Albert Einstein's the most famous example, but I'm sure there are more. I also hear that WWII was very good for the U.S. economy, and if that's the case, deleting that whole event from history might put us in worse economic standing than we are now.
i suppose we could come up with a strict set of rules governing the practice, like Asimov did with robotics. Maybe we could send probes back through time that would let us see and hear the past as it happened, perhaps through some kind of 3-Dimensional interface that let us freely wander the time period... but, i guess, that could also lead to some kind of unforeseen Heisenbergian observational contamination tho.
It must sound like foolishness to you but killing Santa Clause would be easy i'd just have to visit Asia minor at some point between March 16, 270 & December 6, 346 and put a bullet in his head. I know that Atheist don't believe in Santa Clause but historians sure do.
Math and logic are wonderful resources to employ when trying to determine outcomes; but i do agree there are probably a few other things that i would use my Chronoship for.
I think it's safe to say, most of the world, atheist or not, doesn't believe in Santa Claus if we're talking about a fat bearded elf who flies around the world delivering toys for good children and lumps of coal for bad ones.
It's one thing to say there was some dude named Nicolas punching blasphemous bishops earning the title of a saint, but it's another thing to say you believe he became a flying magical fat man originating from Finnish fairy tales.