The end of Shimon Peres's term in July would be an excellent opportunity to abolish the Israeli presidency. It's a largely ceremonial position that costs taxpayers a lot of money. Sure, almost all parliamentary democracies have a separate head of state, either a monarch (e.g., the UK and the Netherlands) or a president (e.g., Ireland and Italy), but just because it's a common practice doesn't mean every country has to follow the same model.
If it were up to me, I would have a three-member presidency. The prime minister, speaker of the Knesset, and the Chief Justice, the heads of the three branches of government, would be co-Heads of State. Some presidential duties would be shared by all three, like signing bills into law, while other duties would be divided between them. The prime minister would be in charge of the more executive aspects of the presidency, such as signing the credentials of Israeli diplomats and receiving the credentials of foreign ambassadors. The speaker of the Knesset would officially appoint the prime minister, comptroller and other positions elected by parliament. The Chief Justice could be in charge of pardons and commutations.
Of course, none of this will happen. Politicians like the idea of the presidency too much. Some of them dream of being elected to the position. For even more of them, having another office they have the power to elect, especially when it is the most prestigious one in the country, makes them feel all the more important.