It's true that the 3 tools share common features. Most setups are fine with any combination of 2 among the 3. It depends what their main purpose is. It's common to accept to sacrifice some caching if you know your application server is fast on statics (eg: nginx). It's common to sacrifice some load balancing features if you're going to install tens or hundreds of servers and don't care about getting the most out of them nor about troubleshooting issues. It's common to sacrifice some web server features if you're intending to run a distributed application with many components everywhere. Still, some people build interesting farms with all of them.
You should keep in mind that you're talking about 3 solid products. Generally you won't need to load balance them. If you need front SSL, then nginx first as a reverse-proxy is fine. If you don't need that, then varnish on the front is fine. Then you can put haproxy to load balance your apps. Sometimes, you'll like to also switch to different server farms on the haproxy itself, depending on file types or paths.
Sometimes you'll have to protect against heavy DDoS attacks, and haproxy in front will be more suited than the other ones.
In general, you should not worry about what compromise to do between your choices. You should choose how to assemble them to get the best flexibility for your needs now and to come. Even if you stack several of them multiple times it may sometimes be right depending on your needs.
Hoping this helps!