Por que Harry Potter não disse a tia Petúnia que ele era rico para melhorar a maneira como ele era tratado por Dursleys?

1. Antes da visita de Hagrid, Harry nem sabia que ele tinha dinheiro.

   "Um -- Hagrid?"
   "Mm?" said Hagrid, who was pulling on his huge boots.
   "I haven't got any money -- and you heard Uncle Vernon last night ... he won't pay for me to go and learn magic."
   "Don't worry about that," said Hagrid, standing up and scratching his head. "D'yeh think yer parents didn't leave yeh anything?"
   "But if their house was destroyed --"
   "They didn' keep their gold in the house, boy! ...
   (PS, Ch. 3, "The letters from no one")

2. Depois disso, ele ainda não percebeu o quão rico ele era até a visita a Gringotes:

   Griphook unlocked the door. A lot of green smoke came billowing out, and as it cleared, Harry gasped. Inside were mounds of gold coins. Columns of silver. Heaps of little bronze Knuts.
   "All yours," smiled Hagrid.
   All Harry's -- it was incredible.
   (PS, Ch. 5, "Diagon Alley")

3. Mesmo depois que ele descobriu que ele era rico, ele não poderia dizer a Dursleys porque ele sabia que eles apenas roubariam seu dinheiro, NÃO seria legal com ele esperando que ele desse o dinheiro a eles :

   All Harry's -- it was incredible. The Dursleys couldn't have known about this or they'd have had it from him faster than blinking. How often had they complained how much Harry cost them to keep? And all the time there had been a small fortune belonging to him, buried deep under London. (PS, Ch 5 again)

   ...

   He had never mentioned his Gringotts bank account to the Dursleys; he didn’t think their horror of anything connected with magic would stretch to a large pile of gold.
   (CoS, Ch4, "At Flourish and Blotts")

4. ... E, mesmo que o fizessem, não poderiam usá-lo em uma sociedade trouxa.

   Harry said nothing. He felt a bit awkward. Stored in an underground vault at Gringotts in London was a small fortune that his parents had left him. Of course, it was only in the wizarding world that he had money; you couldn’t use Galleons, Sickles, and Knuts in Muggle shops.
   (* CoS, Ch4, "At Flourish and Blotts"*)

Harry também não sabia que ele era rico.

Harry vive 11 anos com a impressão de que ele é pobre. Não até o evento do primeiro livro, quando Hagrid lhe mostra o cofre de ouro que seus pais lhe deixaram, ele entende que ele tem dinheiro. No livro 2 vemos Harry empregando o medo de magia de sua família para receber melhores condições de vida durante o verão.

Eu não acho que Harry teria dito a eles depois que ele descobriu sobre o ouro no cofre do banco, porque os Dursleys teriam tentado pressioná-lo a dar-lhes um pouco do dinheiro. Vernon especialmente parece invejar qualquer dinheiro gasto com Harry e pode acreditar que ele deve a eles pelos anos que passou cuidando dele.