The source also mentions dispelling apparent inadvertence (sahw) and dispelling an impression of incomplete inclusion. The speaker reinforces the expression to address specific doubts.
«جَاءَنِي زَيْدٌ زَيْدٌ» — repeating “Zayd” may show that the first mention was intentional, not a slip.
«جَاءَنِي الْقَوْمُ كُلُّهُمْ» — «كلهم» rules out the thought that only some members of the group came.
A useful way to understand emphasis is that it can close off a particular interpretation the listener might entertain. Its benefit is clearest when that possibility is live in the context.