President is a mere Puppet for G-d?

Many years ago I asked a distinguished Talmid chachom whether Gedolim were infallible and he answered if so why is it obvious that Sanhedrin can err?

A similar reply is indicated to those who claim that all leader's are mere puppets of G-d and have no free will.

In Vayikra it states not only the Sanhedrin can err but also a king or any leader

Mishlei (21:01) Like channeled water is the mind of the king in the LORD’s hand;He directs it to whatever He wishes.

Vayikra (04:22) When a ruler has sinned, and done something through ignorance against any of the commandments of the Lord his God concerning things which should not be done, and is guilty;

Berachos (55a) There are three things for which one should supplicate: a good king, a good year, and a good dream. ‘A good king, as it is written: A king's heart is in the hands of the Lord as the water-courses. ‘A good year’, as it is written: The eyes of the Lord thy God are always upon it, from the beginning of the year even unto the end of the year.A good dream’, as it is written; Wherefore cause Thou me to dream and make me to live.

Meshech Chochma (Devarim 17:15): … The Ralbag notes that the heart of the king is in G-d’s hand (Mishlei 21:1). Thus the king has no free will but what he does is determined by G d. Shmuel was thus afraid of Shaul at this point [Shmuel 1 1:11] because Shaul was no longer king and thus had free will to harm him.

Rabbeinu Bachya (Devarim 17:15) It would do well for us to study our history and to learn what happened to the Jewish people during the centuries when their political system was headed by a king of flesh and blood. Devarim Rabbah 5,11 sums it up in these words: the Jewish kings caused many of their people to fall in battle because of their faulty policies. Shaul caused many casualties at Gilboah  David caused a plague. Achav, King of Israel, became the cause of the three year famine. Tzidkiyah’s policies became the immediate cause for the destruction of the Temple . How was it that the entire people who had experienced a tremendous renaissance under the leadership of the prophet Samuel agreed to ask for a king? The Talmud Sanhedrin 20 dissects the wording in Samuel I 8, pointing out that the elders of the people were motivated by pure considerations asking that the purpose of the king be “to judge us,”. The common people were motivated by the desire for their king to be a general who would lead them in war, and their sin was in saying “like all the nations.” They spelled this out in greater detail in verse 20 of that chapter. The people were agreed that they wanted a king, but they differed regarding the tasks of that king.