I was confining my comments to Christian churches.
The PCUSA is MARGINALLY Christian . I have attended a few services at the one near me and NO OUR FATHER was said on those occasions.
I can only tell you that in 30 years of weekly attendance and often mid week attendance I have never heard the Our Father prayed.
It is my guess that the order of services you are looking at are not followed by the majority of the churches of that denomination with any regularity, it is rather like you
taking “St Joseph’s Trinitine missal” to mass. It is a Catholic “prayer book” it is a product of the church but no longer applicable to catholic mass
Protestants do not use “prayer books” in their services.
The Presbyterian Order of Worship includes the Lord's Prayer . . . at my grandparents' church when they were alive, and at my daughter's best friend's church. I have no idea if her church is PCA or PCUSA, but they are considered one of the more orthodox Presby congregations in Atlanta.
Those are the regular prayers and orders of service for those denominations, not outdated or off the wall. I believe you are attributing what appears to be the peculiar local custom of your congregation to Protestants at large.