Well, as to your point about a "new Islamic prophet", that isn't going to happen. Muhammad is traditionally known as "the Seal of the Prophets".
"Seal" in the sense of sealing something shut, like sealing a letter with wax. Muhammad is believed to be the final Prophet/Messenger in a long line of prophets sent by God, starting with Adam (who is a prophet in Islam), and including Noah (Nuh in Islam) and Jesus (Isa in Islam). Jesus is revered as an important prophet in Islam but not believed to be divine, as that is considered blasphemous to Muslims.
In other words, in Islam, Muhammad is the latest and final Prophet ending a long chain of divine revelation, and no other prophet can ever come after him. It's a concept known as the "finality of prophethood".
https://en.wikipedia.org/wiki/Seal_of_the_Prophets
https://fiqh.islamonline.net/en/finality-of-prophethood/
If a person ever did claim to be a "new Islamic prophet", that would be widely considered heretical or blasphemous by most Muslims and that person would be rejected.
(In fact, this has already happened with the Baháʼí Faith, which emerged centuries after the advent of Islam and bases its teachings on both Islam and Christianity along with other faiths. Founded by Bahá'u'lláh, who is believed by Baháʼís to be the latest "Manifestation" of God, continuing a long line of divine revelation that also includes Jesus and Muhammad. It is not accepted by most Muslims. Vaguely similar, perhaps, to how Jews (excepting Messianic Jews) don't accept Jesus as the Messiah or the New Testament as Scripture, or how most mainstream Christians don't accept Joseph Smith and the teachings of the LDS Church/Mormonism or Jehovah's Witnesses.)
As to your point re Islamic holy texts outlining/demanding "this conduct", it's not entirely clear what "conduct" you're specifically referring to. I'm going to take the liberty of assuming you're talking about the stricter applications of Islamic law (Shariah) like corporal punishment and apostasy laws or the much-quoted "Sword" verse (Qur'an 9:5).
As to your first point about people rebelling against the application of Shariah in Muslim-majority countries, again, as I pointed out above, it's a bit more complex. Not all Muslim-majority countries follow/apply Shariah, and some non–Muslim-majority countries including Israel allow certain elements of Shariah in personal civil matters, but it varies by country how much legal jurisdiction those Shariah rulings have in actual law.