They did. First the UAR and Egypt as the UAR dissolved, later, after Egypt-Israel peace, Iraq took up a role. Iran started backing groups that were more extreme Islamists (though still Sunni) that opposed (and often directly fought) the main anti-Israel Palestinian groups, which ended up themselves as the main fighting groups as the peace process took the PLO off the table as a group actively fighting against Israel, and took up an even bigger role when the destruction of Saddam Hussein's regime in Iraq took Iraq off the table entirely, creating both a regional power vacuum and removing the main issue focusing Iran's attention away from Israel.