Should Fantastic Four had been set in the 1960's like X-Men: First Class?

I know the original intention was to set the Fantastic Four in the same universe as X-Men, so that's why it takes place in modern times, but wouldn't it have been better to have set it in the 1960's like X-Men: First Class? The story could have revolved around the space race between the United States and Russia and Doctor Doom could have had a much better origin.