I am not sure if it is covered in the above answer or not, but even when he was alive no one couldn’t have perfectly drawn his picture, let alone now. Thus any picture would have been a lie against the prophet and a big sin. Just like we see many types of Jesus pictures and statues and people praying to Jesus than Allah.
Even if there was a camera at that time, a picture would have been prohibitted due to the certainty that sooner or later people would start praying and asking prophet for help… meaning committing Shirk.
I think there could be other reasons too. When we see a picture, in out mind we draw thousands of words and create a judgement against the person automatically. If there was a picture of prophet some would have drawn a positive and some would have drawn a negative judgement about him based on his looks and some would have tried to manipulate his picture in positive and some in negative color. Focus would have shifted away from Allah, Quran and message of the prophet than his looks.
Even without his picture, in some religious circles, we see people commiting shirk. They are remembering prophet more than Allah… Asking prophet for help and coming close to worshipping the prophet… Just like Christians.