To be fair to squid and nginx, they don't do the same things. Squid is mainly a forward proxy. Nginx is mainly a web server. There's no reason for not using them anymore for these use cases where they excel.
I use haproxy as a forward proxy on my personal computers mainly for ability to control SSL options, sniffing SSL traffic and to support non-SSL enabled clients. I do not need any caching so squid seems inappropriate.