In the brief period in which Chuck Hagel served as the United States Secretary of Defence before being forced to resign this week he hardly left his mark on the Pentagon, America's armed services or the regions in which they operate.

His unhappy tenure, however, served to illustrate some hard truths about the relations between the US and two of its main allies in the Middle East - Israel and Egypt.

The Israeli defence establishment expressed sincere regret at Mr Hagel's departure, Defence Minister Moshe Yaalon describing him as a "true friend of Israel". This was significant considering the fact that his appointment was made in the face of a series of bitter debates in Senate, in which his former Republican colleagues took him to task over disparaging remarks he had made in the past about the pro-Israel lobby and what was seen as his "soft" attitude towards Iran.

That Mr Hagel while in office proved to be one of Israel's most dependable allies in the Obama administration was perhaps, in part, a reaction to that Senate criticism. However, it was likely more due to two other factors which had little to do with him.

With the barely concealed personal antipathy between President Barack Obama and Prime Minister Benjamin Netanyahu, accompanied by a lack of chemistry between their senior aides - as well as a mutual frustration over the quixotic failures of State Secretary John Kerry in just about all his diplomatic ventures in the region - the Pentagon has remained the calm port in the storms.

It helped, of course, that Mr Hagel had less of an adversarial disposition and that as he found himself his frozen out of the administration's inner decision-making, he may have even felt some kinship with his Israeli counterparts. That was particularly true with Mr Yaalon, who has been unofficially boycotted by both White House and State Department for calling Mr Kerry "messianic".

Another awkward ally with whom Mr Hagel was in close contact was Egyptian President Abdel Fattah al-Sissi. Shortly after he came into office, Mr Hagel urged the then commander of Egypt's army not to seize power from the elected Muslim Brotherhood government, to no avail. While some in Washington blamed him for not making the administration's views clear enough, the Defence Secretary successfully maintained the sensitive alliance with Cairo following the coup.

Mr Hagel's ouster has nothing to do with Israel or Egypt. Ultimately he was pushed out because of the lack of a coherent American policy on fighting the Islamic State and as a scapegoat for the Obama administration's failure over Syria. He was appointed to oversee America's retreat from Afghanistan and the downsizing of its military in the post-Iraq War period. He was lost in a power-struggle between the Pentagon generals and a closed coterie of White House senior advisers and, as a result, seen as the wrong man to lead the US military into another war. The irony is that the only senior official who succeeded in maintaining two of America's key alliances in the Middle East is taking the fall for the chaotic state of the administration's policy in the region.