Should you use a VPN while on the same network as the VPN server?

This questions is somehow connected to this other one, where I asked whether it was best to have a dedicated VPN machine or to use the built-in VPN feature of the router when connecting from an external network to my home network.

Regardless of what approach is chosen, does it make sense to use a VPN when you are on the same local network of the VPN server?

I mean, obviously it makes more sense to use a VPN when you are on an untrusted network and you want to secure it, but is there any reason why you should force your local traffic through the VPN server even when you are on your local network?