It's not old fashioned. However, it does mean you have two methods of deployment. In larger ecosystems, a suboptimal release system for some components is less harmful than multiple release systems that have to interact.

I wouldn't suggest moving to docker for this use case, but if everything else was in docker, I'd want this in docker as well, even if that docker container was just running apache.

(Practically, though, if I was starting from scratch, I'd be using NginX.)