Is there any reason to setup and use proxy servers these days?

To control traffic and requests to Servers hosting applications

Tomcat is a web server (can handle HTTP requests/responses) and web container (impiments java servelet API. also called servelet container) in one. Some may called it an application servers but its definitly not an fullfledged java EE application server(It des not impliment the whole java EE API)

Yes...always we need to setup a proxy server on the network.
As with the proxy we can do many things not only cache, we can use the access list and filtering.
O prefer the squid proxy by linux