Freeper bcsco commented that in his church We offer both the chalice and plastic cups.
Plastic cups? For what is supposedly the Blood of Christ? Do the Lutheran churches maintain a sacrarium in the sacristy?
One of my major complaints at my current parish. Back home we used the common cup.
As for the communion on a rotating basis, in confirmation class my old pastor taught it was because many of the old “prairie” churches didn't have a regular pastor, but had a circuit pastor. He would take turns through the month (or longer) going to each parish in a rotation. So (back home) it was the second and last Sunday of the month, which was when the pastor was there in the 1800’s.
My church in college, which was built much later, has communion every Sunday. As does my sister's in Chicago which was built in the early 1800’s but had a regular pastor.