Dynamic subdomains are fairly easy to do actually, you just need to modify your dns.. say
http://person.site.com is really going to
http://site.com/sub.php?this=person
because.. Joomla is not a practical solution to what the OP was asking for. It would cost too much money, time, and effort to hack Joomla enough to allow what he is wanting. Can it be done? Sure ANYTHING is possible... but there are a lot cheaper, faster, and more practical solutions to this.
Most REAL programmers do not rely on Joomla or Wordpress to create websites. They only use it because that is all they know. They would not know where to begin creating a full site from scrath, they do not know anything about PHP, functions, OOP, or anything real programmers have to deal with on a daily basis. They just modify pre-existing code and add ons/modules/extensions/etc that someone else provided.
If someone boasts about how all they know is Joomla, or Wordpress, or __________ then that's basically them telling you that they aren't a real programmer, and if you are asking for real custom work to be done, you better hope that it's part of the "4100 addons".. otherwise you are up shil creek