They’re a part of the mix. Firewalls, Proxies, WAF (often built into a proxy), IPS, AV, and whatever intelligence systems one may like work together to do their tasks. Visibility of traffic is important as well as the management burden being low enough. I used to have to manually log into several boxes on a regular basis to update software, certs, and configs, now a majority of that is automated and I just get an email to schedule a restart if needed.
A reverse proxy can be a lot more than just host based routing though. Take something like a Bluecoat or F5 and look at the options on it. Now you might say it’s not a proxy then because it does X/Y/Z but at the heart of things creating that bridged intercept for the traffic is still the core functionality.
There are some use cases other than web page compatibility. One for me is in dealing with firewall and proxy policy, if the agent is a browser and comes in on specified explicit ports then force authentication, things of that nature.