P.T. Barnum wasn't a song and dance man
I went into this not knowing that it was loosely based on the life of P.T. Barnum. He was the most famous man of his era, thanks in part to his autobiography that he allowed any print house to print, merely to give him more fame. His autobiography was the 2nd most printed book after the Bible.
He was considered a master of marketing and publicity stunts, and inspired Michael Jackson in the 80s to create fantastical tales about his own life (including buying the elephant mans bones, bathing in mineral water and sleeping in an oxygen chamber.)
So I was surprised that 'The Greatest Showman' was about him. They made out that he was 'celebrating humanity' with his freak show. I don't know if that really was the case.
Whatever the case was, I didn't get the feeling that Jackman's character was a genius, a visionary, or master of publicity.
If I were the producers, I would have removed the name Barnum and made it loosely based on his life, but changing details to show that it isn't a biopic (the movie based upon Bill Clintons raise to the presidency, Primary Colors, changed his name to 'Stanton' and changed Chelsea to a boy.)
By changing the names you aren't held to the same scrutiny.