Why didnt this happen in the movie "Aladdin"?

so in the end...Aladdin is telling Jasmin that he cant marry her because he isn't a prince or something....and instead he frees Genie....why didn't Aladdin just give the lamp to jasmine to wish for Aladdin to be prince and at the same time get two other wishes....then when she is done with her wishes, since Aladdin is now a prince, she just gives the lamp back to Aladdin and he frees Genie.....they should have done this....