This is not correct. He didn’t prevent Fatima from having a slave. He instructed her to what was better than that.

Aisha and the rest of his wives didn’t have slaves to the best of my knowledge and if they did,,it was from their money.

ALLAH’S MESSENGER DIDN’T GIVE PERMISSION TO FATIMA, HIS DAUGHTER TO HAVE ANY SLAVE WHILE AAISHA HIS BELOVED WIFE AND OTHERS WERE PERMITTED TO HAVE. PLEASE EXPLAIN