...Google identifies index.php and the site's root as a single page
These two things can totally be different.
...that redirecting index.php to root is not something we should worry about.
I'd personally worry about it because:
index.php is not a friendly URL especially if it has a query string attached to it.
not having a friendly URL could entice hackers in trying to manipulate your site by playing around with parameters and such.
At least if I redirect index.php to root or any other friendly URL page, then I'm effectively masking out ideas for the hacker.
I wonder if leaving things as they are (Without redirecting) is bad for SEO.
You can get a better rank if your URL contains keywords that are part of your webpage (which is why I'd suggest friendly URLs). Also, if accessing http://example.com/index.php and http://example.com result in the exact same page, then redirecting http://example.com/index.php to http://example.com will make your rankings better because you just indicated to google and search engines which of the two copies of content you'd rather display to the user.