Why is the TUX Web Server Dead? Does Nginx/Lighttpd/Epoll/Kqueue Replace it?

Mostly because Ingo Molnár stopped working on it. Why? I believe it was because kernel version 2.2 implemented the sendfile(2) call which matched (approximately) the massive performance benefits previously achieved by Tux. Note the Tux 2.0 Reference Manual is dated 2001.

serving a static file has three steps: decide which file to send, decide if to send the file, send the file. Now Tux did a really good job of sending the file, so so on deciding which file to send, and a lousy job of deciding if to send a file. The decisions are matter of policy and should be done in user space. Add sendfile and I can write a server that will be almost as good as tux in a short time, and add stuff without recompiling my kernel. maybe sql logging. just thinking about userspace sql calls being made from a kernel makes my eye twitch.

Tux isn't required anymore due to sendfile(). Nginx takes full advantage of this and IMO is one of the best web servers for static or non-static content. I've found memory problems with lighttpd, ymmv.

The whole purpose of CDN's is that it moves the 'web server' closer to the end users browser. This means less network hops and less round trip delay, without a large cost to you having to host multiple web servers around the world and using geo dns to send the user to the closest. Be aware tho as these web servers aren't in your control they could be overloaded and the benefit of less hops could be diminished if their network is overloaded. CDN's are usually targets of DDOS attacks and you might get caught up in something that has nothing to do with your content.