Is a satellite system still necessary in new buildings, or is IPTV sufficient?

No! Why should I? I have an internet radio because I can't stand the stations that are broadcast here via FM. My favorite station (Radio BOB) is only available over the internet. Before we finally got our somewhat decent internet connection, everything in the kitchen ran through a SAT receiver.

I don't find an FM radio in the kitchen bad. My previous comment is to be understood in the way that nowadays radio broadcasting is no longer needed in the RF distribution.

I think we will make a compromise and have the wiring installed. Then we will try it via IPTV and if it doesn't work out, retrofit the SAT system. Somehow I can't decide 100% for or against it.

Imho the solution would be much simpler:
Next to the multiswitch with two Unicable and several legacy outputs in the antenna box, one or two Cat6A cables

Which multiswitch have you decided on?

I'll first try out a DUR-line DCR 5-2-4L4, which has two Unicable and 4 legacy outputs. It might be easier/better to do, but a suitable multiswitch currently costs only 20€ less than the converter.

...If your Wi-Fi is too bad for that, then the problem lies in your poor setup...

Sure - a FritzBox 7490 is useless!?! It is mounted quite high in the room - you probably don't even realize why.
Furthermore, there are people for whom radio is not just background noise but actively consumed (Deutschlandfunk, Inforadio, Kulturradio) and who don't want to have to always turn on a TV receiver or buy a new device because no equivalent replacement products are readily available for the existing technology (ME-Geithain and Syrincs - you have probably never heard those names).

Just to estimate:
Everything over IP would easily cost a mere 600€ per year. If not even more.
A complete satellite system with antennas and distributors might cost one-time half that and a new receiver every now and then for at most 200 bucks if you don't want to own a Dreambox.

Sure – a FritzBox 7490 is worthless!?! It is mounted quite high in the room – you probably don’t even realize why.
Furthermore, there are people for whom radio is not just background noise, but actively consumed (Deutschlandfunk, Inforadio, Kulturradio) and who don’t want to have to turn on a TV receiver every time or buy a new device because equivalent replacement products for the existing technology are simply not available (ME-Geithain and Syrincs – you have probably never heard of those names).

The FB7490 is not bad in terms of WLAN, but there are better ones. However, I don’t know why I should hang that ugly thing somewhere high up in the room. For me, the WLAN on the FB is turned off and there is an access point hanging centrally on the ceiling on the first floor. This covers the house much better than the 7490. If better WLAN is needed on the ground floor, then there’s also an access point there. For others with a 7490, we have already installed an access point or are about to install one. If you know a bit about it, you can quite well estimate what works and what doesn’t.

A normal SAT receiver boots up in 2-3 seconds. I don’t accept this argument. Of course, if you have devices that fit that technology (FM or DAB+), then it’s naturally possible, but how many still use this? Internet radio is a view into the big wide world of radio, and for someone without a good internet connection, radio via SAT is the great, simple, and inexpensive way to receive a variety of programs in good quality.

Conclusion: The SAT system is coming, even if we might not use it much later due to the preference for Netflix, Amazon, and others.

Thank you for your opinions!