Think of a framework like Laravel; you can make the Laravel app write "Link" headers for each of the JS or CSS assets declared in its views being rendered. Then, a server, say Caddy which supports push out of the box https://caddyserver.com/docs/caddyfile/directives/push will read the Link headers from the response from PHP, and push them on its behalf. Super simple to implement.

Adoption has been low because there hasn't been enough time for people to get comfortable with and switch to more modern web servers that support this type of thing, and most frameworks haven't figured out that having these sorts of features on by default could have major benefits. But it could happen.