Can we remove template.php from active theme folder?
Here is explained the template.php function:

https://www.drupal.org/node/1728096

If you remove the template.php many things on the theme will stop working, specially all the things that make the template different (or useful). 

But if you're using a subtheme you can remove the template.php in it since your subtheme will use the original theme template.php (As long as you don't have your own hooks and functions in that subtheme template.php).