1) You need a router that supports DHCP relay, which most home routers do not natively support.
2) It won't show you clients that are connected to the Wifi which is probably the majority of clients in most home networks.
3) It doesn't give you the ability to monitor anything beyond the DHCP lease table which all routers show.
So besides wasting 50$, losing a port on your router and having another thing that might break your network down you aren't getting anything.
There is a need for tools that people can use for monitoring the activity on their home networks. All of these IoT devices are going to create problems that need troubleshooting. Yes, the ideas outlined are simple, but this can evolve over time to solve a problem that is going to be increasingly important
i used to do something like this with a freebsd box and had all the wireless clients dhcp to the freebsd box and route through them while turning off dhcp on the wireless router.
ultimately it was a PITA and i run merlin on my wireless router now and it gives me everything i really used the freebsd box for.
and if you have an IOT thing which is misbehaving and you really need to dig into it more than you can with merlin you can always setup ip forwarding on a linux desktop/server/whatever and force the IOT to use that as a router and MITM your own traffic for that box temporarily.