local wg interface does not respond due to the wg-quick script sets up the interface by reusing the local address as the remote address in the ifconfig command:

root@bsd2:~ # wg-quick up wg0
[#] wireguard-go wg0
INFO: (wg0) 2020/02/20 09:45:16 Starting wireguard-go version 0.0.20200121
[#] wg setconf wg0 /tmp/tmp.87viEAsK/sh-np.YdRfI6
[#] ifconfig wg0 inet 192.168.2.2 192.168.2.2 alias

On linux setting up an IP address on a tun interface does not require a remote address:
[root@vpn2 wireguard]# wg-quick up wg0
[#] ip link add wg0 type wireguard
[#] wg setconf wg0 /dev/fd/63
[#] ip -4 address add 192.168.2.2/24 dev wg0

In the wg-quick script function add_addr() is where the assignment is made:
 
 cmd ifconfig "$INTERFACE" inet "$1" "${1%%/*}" alias

I verifed this by replacing remote address with localhost:

 cmd ifconfig "$INTERFACE" inet "$1" "127.0.0.1" alias

Now local ping works. You can give any address I suppose since the ”remote address” of the ifconfig of a tun interface is not really used by wireguard.