the real question is....

I agree... and hindsight is always 20/20. This musical was a huge surprise when it won... but can be explained by many things... which still effect how the voters vote. Streetcar, critically praised, was still considered 'controversial' in 1951... with mostly new, or at least 'Broadway' actors. It was nominated with another very critically hailed movie of the time... A Place in the Sun... made by the very established in Hollywood George Stevens.
Quo Vadis and Decision Before Dawn, both nominated, never really were contenders.
The split in voting between Streetcar and Sun would account for a very admired, and at the time, revolutionary, musical, third runner up, winning.
Also... don't forget... posters always cry 'how could the Academy choose that!'
But it's all a crap shoot.... there is not one body of a few people who make the decision... 'this movie, not that one'... The votes are cast, and the film with the accidentally highest number of votes wins.
If you want even more ludicrous choices for best picture winners considering the other films in their respective years... look to
1952 The Greatest Show on Earth, 1956 Around the World in 80 Days, 1995 Braveheart... to name a few... and yes... I know... it's all a matter of taste.

That question would be added to about 100 other Oscar decisions - like Ordinary People beating Raging Bull or Barry Fitzgerald wining for SA in 1945 over Edward G. Robinson (who wasn't even nominated) in Double Indemnity. They will discover where Jimmy Hoffa is buried before these questions are answered.

How?

As stated in another thread (below), it simply was the irresistable combination of Gershwin's music, as well as Kelly's physical artistry AND beauty. that made the film a killer (yes, even against hot-ass Brando and sublime Leigh breaking legs in an excellent film):

  by gue_dan_iela     (Mon Mar 21 2005 07:58:13)
It enlarges the film, it's just so beautiful and intense...combined with Gene Kelly's genius in dancing we have a great masterpiece.