Is the logic and argument sound?
Let's pursue this answer from the scriptures. One verse or two does not a doctrine make - unless it can be supported by numerous others and eventually the whole bible can be seen to be in concert.
God is Spirit.
Jesus said, 'a spirit does not have flesh and bones a you see I have.'
Therefore God does not have - nor can have, flesh and bones. No one can see God and live Ex 33:20 God is invisible Col 1:15. God cannot become a man or be like a man. Num 23:19 God is not human. God can be represented by a pillar of cloud or a donkey - but these are not God. Whatever OT folks saw or encountered when God was in their midst was a representation or manifestation. Even Adam and Eve only heard God.
While there are many 'proof-texts' that can and are used for many things the bible does not intend, any supposed contradiction must be solved by bringing other scriptures to bear on the proposed truth.
While the OP logic is sound, it is also open to dispute as various ideas are formed by extrapolating the text to mean something extra of one's own making... like, 'God can be flesh and bones'.
What other texts can we use to confirm the proposed logic that Jesus is not a spirit, and therefore, cannot be God? If Jesus is not a spirit, but only has spirit as an addition to himself, then he is a man only. Jesus, like many figures before him may be a god - i.e. a ruler, a mighty person etc. but not the supreme God.
The list of verses showing Jesus has a God is very long. There is one popular verse used to 'prove' that Jesus IS God, Heb 1:8
But about the Son He says: “Your throne, O God, endures forever ...
Ok, that's marvellous, keep reading - the very next verse puts this in context. (context is what should be used to avoid making our own explanations for weird bits of scripture that don't seem to fit properly, or for verses that, on their own, seem to support unbiblical ideas)
You have loved righteousness and hated wickedness; therefore God, Your God, has anointed You above Your companions with the oil of joy.” v9
So Jesus, the son, has a God and this God is not him, but over him, anointing him above all others. When did Jesus ever exalt himself, when did he take a place of authority that was not already given him? Never.
In fact he speaks of this in several ways. Being the son of God - holy pure etc., he didn't regard being equal with God something to grasp after, but took the role of a slave, a servant OF God - even to death on a cross.
Satan is the great usurper. Jesus the exact opposite, always choosing the humble path, knowing all the while he was destined for great glory being the one planned for from the beginning. Even though he was at times pushed to the limit, seeking the Father find another way (take this cup from me), he again humbly and obediently chose the Father's will. That Jesus has his own will, makes him not God. Heb 1:9 makes him not God.
V1 of Hebrews 8 is also important for context.
God, after He spoke long ago to the fathers in the prophets in many portions and in many ways, 2 in these last days has spoken to us in His Son, whom He appointed heir of all things, through whom He also made the ages (not world or universe).
So the son is not Yahweh of the OT. Now that the son is around, having been born of Mary, He speaks through Jesus.... who He made heir! If the pre-existing logos/son made everything (hence the 'world' bias end of v2) why is he now made heir? If he is 'made' heir, he wasn't the heir before.
Jesus qualified to be heir after finishing his mission without error or blemish, becoming the perfect Lamb. The Lamb who would have died, regardless of the cross, if just once, he had put his will before the Father's. His total dependency through pray ensured his success. Who was he praying to? The supposed eternal son, who is God, is praying to Himself? Please, it makes a mockery of what Jesus accomplished.
In the days of His humanity, He offered up both prayers and pleas with loud crying and tears to the One able to save Him from death, and He was heard because of His devout behaviour. 8 Although He was a Son, He learned obedience from the things which He suffered. 9 And having been perfected, He became the source of eternal salvation for all those who obey Him Heb 5:7-9
Having finished the course, he is now given a new life force - to have life as the Father does. John 5:26 a life he didn't have before - being mortal and subject to death. Rom 6:9
You have put all things in subjection under his feet.” For in that He put all in subjection under him, He left nothing that is not put under him. But now we do not yet see all things put under him. Heb 2:8
Again this Jesus, who is not God, is given rulership (by God) he didn't have before, and is still waiting on its grand fulfilment at the close of this fleshly age.
Therefore having a great high priest having passed through the heavens, Jesus, the Son of God, we should hold firmly to our confession. Heb 4:14
Jesus, who is not God, has entered the heavens. What? Wasn't he already there eternally?
Clearly, the writer of Hebrews thinks it's a wonderful addition to Jesus' accomplishments. No man has ever gone to heaven - the 'place' where God resides. Echoed in Eph 4:10
He who descended is the very One who ascended above all the heavens, in order to fill all things. (that weren't filled before by the son)
We can understand 'descended' as the heavenly man he was being holy and without sin. This is not an 'earthly man' as all other men are. Jesus was 'sent' from heaven, just as the manna and all other Godly gifts come from heaven. As the 'heavenly man, God cannot be a man, so this makes perfect sense.
Now Jesus is at God's right hand. Not the Father's right hand. So either the writer is confused and God including the Son has the other son Jesus next to this 3in1 God. OR Jesus is the man, made just like us 'in every way' Heb 2:17, made Lord and Christ, made heir, exalted above all others, given life like the Father has, who was tempted just like us, died like us, raised like us in a new body that is not spirit but powered by spirit to have life eternal at last!
Oh we could go on and on, but also notice in Heb 2:17, made like us in every respect... that, 'he might become a merciful and faithful high priest in the service of God'.
There are a zillion texts that in concert agree that Jesus is not God but His magnificent son. The fleshly man of God's logos - the word, the plan and purpose of God to be the Saviour of all through his humble and obedient life and sacrifice, foreknown and foretold.
The OP argument is therefore sound and accurate. Not only does it stand alone by logic, but it is well supported by myriad texts that speak the same truth.
Any random 'proof-texts' that some might offer to oppose this plain speaking God and His apostles is reading in more than intended or taking them out of context to make them say whatever they want and find way too many verses opposing.