They probably don't want it because it means storing uneccesary data, and with multiple accounts, one can play against their second account and fix the game, gaining undeserved rating points.
Chess.com doesn't tell us their methods of creating +1 accounts, but I think it has something to do with the IP address, similarities between contact emails which you give to chess.com when you start playing (e.g. one accounts email can be fake1@gmail.com, and the second could be fake2@gmail.com)
@OP: This link will provide helpful information.
http://support.chess.com/Knowledgebase/Article/View/15/1/can-i-have-multiple-accounts
People create multiple accounts to cheat. They play games against themselves, and then have one account resign to the other a bunch of times, in order to increase their rating.
How does chess.com tell if you have multiple accounts? Easy. As you can see, I have 23 accounts, and you have 83 accounts! JK
I joined few minutes back. It said a person cannot create multiple accounts here. Why would a person create multiple accounts, and how would chess.com know that a person has created multiple accounts? Just asking out of curiousity.