Therefore, stating "you do NOT need a router" is incorrect. If you want to share your internet connection amongst multiple users (either via Ethernet or WiFi), then you DO need a router.
I will go back to my ADSL modem and switch combination and explain to it that it can't possibly work. Even though it has been in use for a number of years.
Perhaps my stupidity paid off.
A router is a multi-user device that presents an ethernet port on the user side. A router incorporates an embedded modem.
Not the one in a place I volunteer. Ethernet comes out of the wall into the router. The institution somehow provides the Ethernet port on the wall. A fixed IP address is assigned. The router provides 4 Ethernet user ports and WiFi.