You make good points in the OP. If more Christians would put their own heart and effort into showing the world what Christmas means to them, these discussions would be completely overshadowed.
However, the issue of displays on public property is more one of politics and freedom than it is about religion. It’s the same thing with allowing the boy scouts to pray or any of the other issues that the supreme court has (only in recent times) thrown into contention.
The supreme court has chosen to replace “government of the people, by the people, for the people” with “government of the people, by the establishment of the elite, for the special interests of the establishment”.
Take for instance our public school funding. We the people are good enough when collecting taxes, but not good enough when disbursing the funds. The government happily takes money from Catholics, Baptists, Methodists, Episcopalians, Jews, Muslims, Wiccans, Agnostics and secularists. Then when they have to give the money back to educate the children they tell us “you can have this money only if you send your children to the secularist school”. The money came from “we the people” but “we the people” don’t get to decide. Same as with the funds “we the people” paid to build city hall.
The constitution says that the federal government will stay out of religion and leave it up to locals. But the supreme court conveniently “interpreted” that clause to say we must separate church and state (however they want such a separation to be carried out). This taking of power away from the people is what the contention is all about when it comes to local nativity displays or prayers of the Boy Scouts, etc.