It is enough for him to say “I submit” because submission is only for Allah . However, Prophet Ibrahim u said, ﴾أَسْلَمْتُ لِرَبِّ الْعَالَمِينَ﴿ “I have submitted [in Islam] to the Lord of the worlds.” and this is the difference between the words of Allah and the words of His slaves.
Islam has an all-encompassing meaning consisting of humbling oneself to the commands of Allah, and to entrust your affairs to Allah . We say that humbling oneself to the commands of Allah is entrusting one’s affairs to Allah . And by this meaning, all the revealed religions are actually Islam.