Yes, people are people and will find other reasons to fight.
But this has been a big one which has echoed through the centuries. What might be a top 20% possibility over how much change we might reasonably expect?
I think it's possible that you could have had the early church adopt a less specific, more flexible definition/relationship of God, Christ, Spirit. It seems like the most likely POD would be if Arianist-type Christians were a larger portion of the overall population of Christians AND of the clergy leading up to the Nicean Council. If you have that, then the Church leaders might have been less emphatic on that point and Constantine might have wanted to keep the definition broad to enhance the unifying effect of the religion on his empire.
If, instead of it's current composition, the Nicene Creed essentially said, we believe in:
- God, the Father Almighty, maker of all things
- The Lord Jesus Christ, begotten of the Father, who for us and our salvation came down and was made man, suffered, and on the 3rd day rose again into heaven
- The Holy Ghost
If it left out some of the other specifications of relationship, what begotten means, etc, you could have a 'bigger tent' of belief that wouldn't define things like Arianism as heresy.
You're right that people would find something else to argue about, but there are a lot of arguments even today where one group calls another "non-Christian" because their interpretation of the Trinity is different, even if 90% of their other beliefs are incredibly similar.