I am not an expert on lore, but i think there are some factors that can be taken into consideration when assessing perhaps her wealth and lifestyle:
A) Alderrans financial role in the Rebellion.
B) Her lifestyle as a princess
C) Her dedication to the rebellion
A) If i understood from the movies, Alderran was not seen by Tarkin as a tool of pursuasion, but as a suspected threat. Although i do not doubt that the Grand Moff was a ruthless man willing to destroy a planet to break a princess, I feel that Alderran, and Leias Royal family were major background supporters of the war effort. In destroying the planet, Tarkin was cutting off a huge source of support for the rebellion.
B) She was an only child. And so that means she was the sole heir to the throne, and whatever wealth that might have carried with. As a ruler over the wealthy Alderran people, she certainly was no enterprising business woman intent on profit, but definitely had access to the wealth of the planet.
C) However, coming to the last part, I feel that she wanted to be much more of a front line player. While im sure she had the ability to sit safely on Alderaan and send funds under the table to the Rebellion (which is of immense importance to any large scale rebellion), she chose to carry the plans to the death star at the risk of being captured and imprisoned, led the strike force on Endor, and freaking infiltrated Jabbas palace to get back Han. She was no meek progressive, passively resisting the Empire while lounging on Alderaan, but actively amd passionately pursuing the ideals and people she believed in.
Leia probably had the wealth and power to be a "1%-er", but definitely did not live her life like one.