I can't understand why embedding code in webpages is so widely considered a special ability of PHP which Perl lacks when that is such a basic built-in feature of mod_perl.

Because "mod_perl compiled with the SSI option" ne "perl".

Because the "out the box" experience with PHP for the web for most people is a Apache already enabled with mod_php. For Perl it's the good old fashioned cgi-bin directory.

Yes, Perl can do all that PHP can do. Yes, in many cases it can do it better from a certain technical perspective. But for most people getting up and running with PHP is way easier than getting up and running with mod_perl.