Broadband connection / TV, radio, LAN in every room?

Here Traumfänger probably got something mixed up. The broadband modem does not necessarily have anything to do with WLAN. No matter what the device is ultimately called (modem, router, Connect-Box(tm)),

: You are right there, thanks for the clarification of terms. Indeed, modem and WLAN router can be two physically separate devices and have different functions. I only use it as a combined device now, but it doesn't have to be that way.

These make the WLAN unnecessarily slow. Instead, it is better to connect an access point (in a strategically favorable location in the house) by cable to the aforementioned switch.

Yes, you are right there too, I see it the same way:

Whereas in the past, the transmission capacity via cable was usually higher than via wireless network (WLAN).

In the future, I will only use WLAN for phones / iPad and for a guest access. That is why CAT7 cables are everywhere (currently still with CAT6 sockets, ). Your solution with the access points is certainly more performant than a WLAN repeater, I hadn't even thought of that. Thanks for the hint.