It's important to remember that at the time Grant landed on the $50, portraits on bills changed regularly. A lot of specific bill releases only lasted a single year. There were also a multiplicity of notes, Silver Certificates, Gold Certificates, Treasury Notes, etc. frequently with different portraits on all of them
Are you a fan of William Fessenden, former Secretary of the Treasury? Not a problem he was on a $20 in 1882. How about Civil War general Phillip Sheridan? He's on a $10 in 1890 and a $5 in 1896. Names like Martha Washington, Daniel Webster (not the famous one), Running Antelope, Justice John Marshal, Merriweather Lewis (explorer), Robert Fulton (inventor), and more, all graced notes in the later 19th century.
As a general or president, Grant absolutely qualified as the type of person who showed up on notes. He was on a $5 in 1886 and 1896. He got a $10 in 1899, and showed up on a $50 for the first time in 1913. So he was just yet another individual who showed up on bills from time to time; one among dozens.
This was all finally cleaned up in 1928 when the US created a series of notes that were consistent in size and style, and carried the same portrait on the reserves notes, silver certificates, and gold certificates. It also was the first time that the current set of familiar portraits were used together (Washington on the $1, Jefferson on the $2, Lincoln on the $5, and so on). If the US had followed their usual practice the portraits would have changed. But the frequently of change had already slowed to a crawl in the 1910s and 1920s. After the 1928 series was released, they stopped changing at all.
The men on 1928 series weren't particularly special. They were just the ones in rotation when the rotation stopped. Certainly Hamilton and Franklin probably also wouldn't make the cut of 7 most likely to be put on bills if we were picking from scratch today. And Jackson wouldn't be included due to his controversial status today.
Basically Grant is on the $50 because he got on the $50 when it was easy to do so, and then kind of got grandfathered in when they stopped changing.