Is there any reason why I shouldn't install Java?
Installing java won't have much effect on battery life. 

I don't think installing Flash will have much effect either.

Where the issue is is when you hit a website with badly written flash (and to a very much less extent Java) where the animation takes up CPU but you can just leave these sites - you will be no worse off than not installing.

Java is now rare on websites and not really used for parts of the web site the user does not need.

I think a better way is to install a plugin for your browser like ClickToFlash which stops Flash loading until you tell it.