Not exactly...
My way leaves us with three distinct members of the Godhead.
Your way... It leaves a solo (not a Trinity) with God wearing three name tags.
God the Son is distinguished from the Father.
Distinguished by having his soul in union with God.
His Soul, being God's means to express God to men, in a manner that men (who are souls) will be able to relate to.
John 1:18
No one has ever seen God, but the one and only Son, who is himself God
and is in closest relationship with the Father, has made him known.
[He has revealed Him and brought Him out where He can be seen;
He has interpreted Him and He has made Him known].
That is what the Soul of God the Son does on our behalf.
So that we who are souls can have God perfectly interpreted to us (in human speak)
to be understood by we who are souls in a manner we can relate to.
Those who do understand what I am saying usually have a peace accompanying what they perceive.
It angers others. They must find reasons to justify themselves in their anger...
Easy to do...
"Heretic." Without understanding a word I am saying.
That thinking is knowing how those who are fighting the good fight remain good while fighting.
................. Would you like some fries with that?