Your point is correct, but what’s your source material on Mohammad? My understanding is that the Koran was assembled from parts written down after much retelling long after his time, and it originally appeared in multiple versions until an Egyptian printer made a “standard” edition in the 20th century. His “biography” was spun up a century or more after his supposed life and death. Most of the source material comes from reports of purported “sayings”, many of them actually created by lawyers as legal arguments. The Mohammad legend is mostly a fabric of lies that evolved Mohammad into a God-substitute* used to market their new religion and a provide legitimacy for “Islamic” regimes, first under Khalif Abd al-Malik. My point is that describing Mohammad as a prophet, thug, 1st homo, later homo, pedophile, etc., is a leap of faith. Nothing verifiable is known about him.
*Blasphemy is generally understood to be abuse directed at God. For example, Christians and Jews don’t think “using in vain” the names of prophets Isaiah or Moses in vain is blasphemy. The Muslim obsession with those who blaspheme Mo has definite implications about whom they worship.
My source material on the self-proclaimed prophet (profit?) is Islamic writings and tradition. Even by their own estimation, he was not someone civilized people would admire today. He is said to have married his favorite wife, Aisha, when she was six years old, but as a generous and gentle man waited until she was nine to consummate the “marriage”.