When did that idea first take hold?
In the original 1964 PLO Charter, Jerusalem is not mentioned once.
In the 1968 PLO Charter, after Fatah dominated the organization, Jerusalem is still not mentioned once.
In Yasir Arafat's 1974 speech to the UN, he demands a single Arab-dominated state to replace Israel, but he does not say that Jerusalem must be its capital.
The earliest mention of east Jerusalem as the capital of a Palestinian state that I could find in an official Arab document was the 1982 Fez Initiative, an Arab peace plan that was ambiguous enough to make it sound like it might have indirectly recognized Israel.
And the 1988 Palestinian "Declaration of Independence" then went on to declare that Jerusalem was its capital.
If Jerusalem is so key to the establishment of a Palestinian state, why was this not mentioned before the 1980s?