"The Vulcan Science Directorate has determined that time~travel is impossible."
- Commander T'Pol
Now assuming that that ain't true... Mucking about with time is bound to be an all around bad idea. Time unfolds the way it does for a purpose and a reason.
While I may not like how events turned out, I did come away from every experience with a bit more knowledge and was slightly changed by each event accumulating into what and who I am today.
We are each a product of the net sum of our experiences, to lose one or replace one experience changes who and what we are, sometimes a single event can have profound impact on who/what we are.
I believe that even being an observer tends to affect how time unfolds. Thus no time traveler can go back in time and observe. Their mere presence standing on the street could cause a person to have to side step and that fraction of a second could change the course of their whole history.
And to purposeful muck around and do something to cause change - very troublesome.
Be it the Grandfather Paradox (going back and killing your grandfather before he has kids - does that mean your parent and you never existed? If so then how did you manage to exist to kill your grandfather?).
Or be it something noble like killing Hitler before he got Germany's panties in a collected bunch to take over the world.
While that last may not lead to paradox, it could have a far worse outcome than what WWII had.