The Trouble with Time-Traveling Assassinations

My views on time travel were largely shaped by an episode of the Twilight Zone in which he discovered that you can't change the past via time travel because the time travel that will happen has already happened in the past.

Anyway, the stereotypical use for a time machine, other than delivering a witty comeback, is to kill Hitler. (Why does no one ever travel back in time to kill Stalin or Mao? Why is it always Hitler?) Here's how I see that working out:

You take the time machine back to kill Hitler.

Some neo-Nazis take the time machine back to protect Hitler.

You bring big weapons.

They bring big weapons.

You bring some help.

They bring some help.

You bring advanced technology to the Allies.

They bring advanced technology to the Axis.

Suddenly, the plot to kill Hitler makes WWII several times worse.