Instead of the Prophet Muhammad (peace be upon him), it is authentically proven from Sayyiduna Umar bin Khattab (may Allah be pleased with him) that he used to begin the prayer with a supplication similar to the one mentioned in the hadith of Harithah (may Allah have mercy on him). I do not dislike beginning the prayer with this supplication «‏‏‏‏سُبْحَانَكَ اللّٰهُمَّ وَبِحَمْدِكَ» ‏‏‏‏ because it is proven from Sayyiduna Umar Farooq (may Allah be pleased with him) that the Prophet (peace be upon him) used to begin the prayer with this supplication. However, I prefer beginning the prayer with this supplication more, and that is more deserving of being acted upon, which has been narrated with a connected chain from just narrators from Sayyiduna Ali and Abu Hurairah (may Allah be pleased with them both) in the hadith of the Prophet (peace be upon him). Because following and adhering to the Sunnah of the Prophet (peace be upon him) is superior, higher, and better than following the Sunnah of other individuals.