This reminds me of trying to play Half Life Alyx on an Oculus.

Doesn’t need to be the case if you segment your network to protect against ARP.

Don’t have the Wi-Fi network “upstream” of the LAN. You want the connection between the LAN and Wi-Fi to be through the WAN so you get NAT protection.

The risk is the ISP Wi-Fi. As long as you’re using WPA with a good long random passkey, the risk is minimal. However, anyone who had access to your Wi-Fi could initiate an ARP spoof (essentially be a man-in-the-middle)

ETA: the ARP table in networking is a cache of which IP is associated with which MAC Address. By “poisoning” or “spoofing” this table in the router and/or clients, a bad actor can see all unencrypted traffic.

As an FYI: this set up is vulnerable to ARP spoofing. I personally wouldn’t use any ISP-owned routers other than for NAT.