one of the benefits of using a packet switched solution is that it’s expandable in the future… adding extra terminals anywhere there’s networking is pretty powerful - you can change your mind about location, or even technology in general and not have to worry
… and it’s probably much easier to extend on in the future too - say open source AI assistants get better, you might want to build one that integrates with timers etc, that’s much easier with packet switched … or even more likely, you want to broadcast to the intercom from outside your house or even just make mobile phones able to be transmitters inside the house
you’re totally right that simple point to point intercom stuff like that is a much simpler solution, but packet switched is king for a lot of future-proofing reasons - perhaps not something that OP cares about (a project completed is better than a perfect plan not begun), but worth mentioning
expanding on this, depending on technical skill level:
i’d probably get some SBCs like raspberry pi (or cheaper; raspberry pi is probably overkill here!) to be the terminals, run asterisk and have an extension for each terminal… run a voip client that automatically picks up any call it receives, and connects to a mic & speaker, connect a button to GPIO and write a script to call a conference extension for all devices (or multiple buttons for multiple extensions to call individual locations)… i’d probably add a second button for a “call back”-like feature - a terminal broadcasts a message and there’s a button to reply only to the terminal the last call was from
this would allow you to use phones as terminals too - even receiving “calls”, although in that case the caller would have to wait for the phone user to pick up - just like a regular phone. probably more useful as a transmitter
all of these things aren’t super difficult in isolation - probably setting up asterisk is the hardest part