Aren't most PHP sites out there running mod_php anyway?

15 years ago absolutely. Most modern sites will be running php-fpm (or maybe FrankenPHP)

Yeah, I don't think I've touched mod_php ever since Apache 2.4 came up with mod_proxy_fcgi, allowing dead simple integration with php-fpm.

PHP does need to invest more in the built-in web server, though. Last time I checked, they still recommend against using it in production.

All other popular runtimes provide a standards-compliant HTTP daemon that any other HTTP daemon can proxy to, it's just the way things work nowadays. Insisting on FastCGI limits integration with more modern web servers and HTTP-speaking middleware.