Do Biblical Unitarianism and the orthodox Trinity doctrine differ soteriologically?

In Biblical Unitarianism, Jesus Christ is a mere man, maximally inspired by the Holy Spirit. Therefore, a mere man died on the Cross, was resurrected, and now sits at God's right hand. How does this differ soteriologically from the orthodox Trinity doctrine? As I understand it, in this doctrine, the Father, Son, and Spirit are a single immortal (cannot die) and immutable (cannot suffer) Being with a single mind, will, and consciousness. Therefore, the Son did not die because he cannot die. Chalcedon explained this as that Jesus Christ has or had two natures and only the human nature died. So, in both Biblical Unitarianism and the orthodox Trinity doctrine, it was a mere man who suffered and died on the Cross. Is there a difference between the two systems in terms of why Jesus had to die? Some of the comments below deny that the Trinitarian God is a single Being with a single mind, will, and consciousness. Therefore, I add the following: The orthodox Trinity doctrine is often explained to people by saying that the Father, Son, and Spirit are one God existing as three Persons. The phrase “three Persons” implies three distinct minds. However, in the Trinity doctrine, the Father, Son, and Spirit share a single mind and, therefore, a single will, consciousness, and self-awareness. They do not each have a distinct mind. For example: > “When today we speak of person in the plural, we think almost > necessarily, because of the modern meaning of the word, of several > spiritual centers of activity [minds], of several subjectivities > [biases, views] and liberties [freedoms].” (Karl Rahner, a leading > Catholic scholar, in ‘The Trinity) > > “There are not three of these in God. … There are not three > consciousnesses; rather the one consciousness subsists in a threefold > way. There is only one real consciousness in God, which is shared by > the Father, Son, and Spirit.” (Rahner) > > “The element of consciousness … does not belong to it [the Person] in > our context [the official doctrine of the {Catholic} Church].” > (Rahner) > > “There exists in God only one power, one will, only one self-presence. > … Hence self-awareness is not a moment which distinguishes the divine > "persons" one from the other.” (Rahner) > > “Each Person shares the Divine will … that come from a mind. … Each > Person's self-awareness and consciousness is not inherent to that > Person (by nature of that Person being that Person) but comes from the > shared essence.” (Rahner) > > “We must, of course, say that Father, Son, and Spirit possess > self-consciousness and that each one is aware of the other two > ‘persons’. But precisely this self-consciousness … comes from the > divine essence, is common as one to the divine persons.” (Rahner). Lewis Ayres stated similarly that the Persons do not “possess different natures, wills, or activities.” > “We can now try to summarize how pro-Nicenes conceive of a divine > person in the abstract. … We cannot … assume that they possess > different natures, wills, or activities within the one Godhead.” > (Ayres, p. 295) [Lewis Ayres, Nicaea and its legacy, An Approach to > Fourth-Century Trinitarian Theology, 2004] Consequently, leading Trinitarian scholars confirm that it is misleading to describe the Father, Son, and Spirit as “Persons.” > “The champions of the Nicene faith … developed a doctrine of God as a > Trinity, as one substance or ousia who existed as three hypostases, > three distinct realities or entities (I refrain from using the > **misleading** word' Person'), three ways of being or modes of existing as > God.” (Hanson Lecture ) > > “By the conventions of the late fourth century, first formulated in > Greek by the ‘Cappadocian Fathers’, these three constituent members of > what God is came to be referred to as hypostases (‘concrete > individuals’) or, more **misleadingly** for us moderns, as prosōpa > (‘persons’).” (Anatolios, xiii) [Khaled Anatolios, Retrieving Nicaea, > 2011] The orthodox Trinity doctrine is sometimes explained, using Greek terms from the fourth century, as one ousia (substance) and three hypostases. But the term hypostasis is also not appropriate because, while the Father, Son, and Spirit in the Trinity doctrine are a single Being with one mind, the Greek term hypostasis means something that exists distinctly from other things: > An "individual existence” (Hanson, p. 193); "Distinct individuality" > (Hanson, p. 53) "Distinct reality" (Hanson, p. 190); “Something that > really exists, and exists in itself, as distinguished from an accident > or a quality;” (Lienhard) "Distinct personalities," "distinct > existences," and "to be existent." (Litfin) “Concrete individuals” > (Anatolios, xiii) In the Trinity doctrine, the distinction between the Father, Son, and Spirit is invisible to the created universe. The creation only sees one Being: > “By the last quarter of the fourth century, halting Christian attempts > … had led … to what later generations generally think of as ‘the > doctrine of the Holy Trinity’: the formulated idea that the God … is > Father and Son and Holy Spirit, as one reality or substance, > **operating outward in creation always as a unit**y, yet always internally differentiated by the relationships of origin that Father > and Son and Holy Spirit have with one another.” (Anatolios, xiii) > > “The distinctions between them are real: but we do not know what it is > to exist distinctly in this state.” (Ayres, p. 295) So, if the terms 'Persons' and 'hypostases' are misleading and the distinction between them is invisible, how should the 'Persons' in the Trinity doctrine be described? Hanson refers to the Father, Son, and Spirit as “three ways of being or modes of existing as God:” > “The champions of the Nicene faith … developed a doctrine of God as a > Trinity, as one substance or ousia who existed as three hypostases, > three distinct realities or entities (I refrain from using the > misleading word' Person'), **three ways of being or modes of existing as > God**.” (Hanson Lecture ) One might respond and say, yes, that may be the orthodox Trinity doctrine, but I believe in a Trinity of three Persons with three distinct minds. That would be consistent with the Bible, but if the three Persons are equal, there would be three Gods (Tritheism). As soon as one speaks of three Minds, two of the Minds must be subordinate to the other; otherwise, one has three Gods. But to admit that the Son and Spirit are subordinate to the Father would be 'Arianism.' To avoid both Tritheism and Arianism, the orthodox Trinity doctrine has to say that the Father, Son, and Spirit are a single Being with a single mind.