No one thinks you can actually write an infinite list.
What it means for there to be infinitely many natural numbers is that for any finite list, there are natural numbers not on that list (something you appear to agree with). If there were finitely many natural numbers this wouldn't be true
Sure they do. Cantors argument, infinite sums, mathematicians keep using infinite lists as if they do exist.
Let’s not even begin about the axiom of choice. Or transcendental numbers.
You're also treating the natural numbers as infinite if you think there can't be a finite list containing all of them
Depends. Not the way I look at them. But this discussion is getting off topic (my own fault), so perhaps we should continue it somewhere else.