Salah is an order by Allah and has to be performed in the manner which HE has obliged us to.
However, we do not know how Prophet (s) was ordered to offer his salah. It could have been like ours or something more for himself.
Regardless, it isn’t a taboo to send salutations on the self. We have several instances that one can send salutations on self like when you enter your house and say a loud Salam even if there is no one in the house-at the time, and the Salam is solely meant for yourself.
Besides this, in salah after you send salutations on prophet, you send one on your self and the rest of the good servants of Allah too and it shows that it’s perfectly ok to do so.