The number of function calls during a single page view can be quite a lot. I don't know the number, but my guess is that it's several thousand. If you want to log all of this data, you shouldn't post it to the screen, but instead write it in a file, like the
dd function that the
devel module has.
If you want to log all function calls, you should start by the end, that last function that is called in a drupal page. One of the last functions where you could start is
drupal_page_footer. You can add the
debug_backtrace in that function.
Then you would have to go through all the functions and add
debug_backtrace for all the functions that those functions call. Then you would have to go through all the new functions listed in the
debug_backtrace you just added and repeat the above step until you or your computer chokes.
It's possible to do this, but to get anything useful you will need a profile tool, which can do all of this in seconds instead of hours. This is where computers excels: recursion.