Why can't Yellow Jersey change hands on last day of Tour De France?
Tradition, and the layout of the final stage. 

Tradition holds that the last stage is a victory parade for the GC contender, and the yellow jersey. Cadel Evans rode a good part of the 2011 final stage, once in Paris, with champagne in hand.

In addition, the layout of the stage, a 95 km flat ride finishing with multiple laps around the Champs Elysees, and culminating in a bunch sprint, rarely allows the opportunity for any major time to be gained. So unless they are within seconds, as in the 1989 Greg Lemond win by 8 seconds over Laurent Fignon, the last stage will rarely play a part in the GC standings. 



As is stated in the description of the stage on the letour.fr page today:


  Every other time, it has been a road stage that has been decided in a bunch sprint, except on four occasions. Those exceptions were the victories taken by Alain Meslet in 1977, Bernard Hinault in 1979, Eddy Seigneur in 1994 and Alexandre Vinokourov in 2005. It is incredibly hard to get a telling gap on this stage when breakaway riders are always within sight of the peloton.”


If you know that a breakaway will not gain you minutes, why risk the ire of the other riders, and your public by messing with the traditions of the race?

One of the things that has always brought an audience back to this race above all others are the traditions of fair play and honorable conduct that are embodied by traditions like the one that allows a crashed race leader to regain his time by the other riders, before the race continues. These unwritten traditions are not rules, but they make this race special.

Combine the two, and you will rarely see a major change on the last day. It can, and does happen. Just not often.