In case there is a security hole in their Webserver (Apache, Nginx, HAProxy, etc) or their application (Wordpress, etc), that an attack cannot escalate privileges even further. Image someone manages to execute arbitrary PHP code, now they can gain gain root access, read private keys, etc. Things PHP should not have access to.
For spectre, the consequences of not applying those patches are not as bad but it wouldn’t surprise me if you could still do a lot of harm. PHP is somewhat sandboxes these days (by using chroot and what not) and meltdown/spectre could be used to escape the sandbox.