It wasn't due to Pershing being "better" than any of those other generals, but rather due to a legal loophole that only allowed Pershing to keep his rank as a 5 star general by being given that title

Pershing gained the rank of Commander of the American Expeditionary Force, a position which could only be held in wartime emergency, or while occupying a specific office (such as Army Chief of Staff). Due to the end of the First World War and therefore the end of the state of emergency, Pershing was going to lose this position and be reverted back to a standard 4 star Major General rather than the commander of the whole AEF. In order to prevent this from happening, President Woodrow Wilson signed Public Law 66-45 stating:

"That the office of General of the Armies of the United States is hereby revived...[for] a general officer of the Army who, on foreign soil and during the recent war, has been especially distinguished in the higher command of military forces of the United States...and any provision of existing law that would enable any other officer of the Army to take rank and precedence over said officer is hereby repealed"

This bill was rushed out in only two days in order to be in effect when Pershing returned from France, so that he could be given his new commission the moment that his emergency grade expired. Being appointed General of the Armies would allow Pershing to continue outranking all other 4 star generals until his retirement in 1924.

In WW2, with the creation of the Combined Chiefs of Staff, American 4 star generals were now being outranked by British 5 star generals, creating a push for a new 5 star ranking in the US military. It was proposed to give it to Marshall, but he denied it, saying that such a high ranking was unnecessary as being given that rank would mean he would outrank every other general in the army like McArthur and Eisenhower. In September 1944, the War Department finally allowed a five star grade to be granted to generals, which would be enacted that December in Public Law 78-482. This new title was referred to as "General of the Army", which would be held by a number of generals since then, such as Marshall, McArthur, and Eisenhower.

The title of General of the Armies wasn't changed, allowing a position which out-ranked five star generals to remain a possibility should it need be, but as of now nobody has been promoted to that position outside of a short push to give it to McArthur in 1955, due to the controversies that would be created from essentially downgrading all other five star generals.

Well politics is the answer. I don’t think any serious military historian would rank Pershing closely to Grant. We also know that no way in hell would a posthumous promotion for Grant, arguably our nations best military commander, to General of the Armies, would stand a snowball’s chance in hell of passing through Congress as Southern politicians would quickly squash it.

Pershing was the U.S. Commander of the largest war the U.S. had been involved in up to that time and he was a winning general of the largest military conflict in human history up to that time. Pershing also held huge public appeal at that time. His personal looks with his broad jawline, jutting chin, eagle eyes and rigid military posture and physical fitness he was the perfect picture of a determined military commander. So Pershing had huge public appeal. So flush with American victory in WWI it was public sentiment of the time that the great hero of the moment be given this honor. The reason the 5 star Generals of WWII rejected the promotion in deference to Pershing is that most of them served personally under Pershing who mentored them and advanced their careers.

Ultimately the highest ranking Commanders in U.S. History are Washington, Grant and Eisenhower as they also achieved the rank of Commander in Chief of the U.S. Military. Which I think is fair as all three Commanders so achieved a resounding greater peace with their victories and the American public recognized that as the ultimate mark of a great General.