Public ip is useful if you are hosting something at your home. Coz for me I am living abroad if want to watch axtro go, I can openvpn to my home router and watch as I am in MY (axtro is blocking commercial vpn btw), or u host movie then u setup ftp server u can access it thru ip address assigned by your isp + port forwarding.

If private ip, u cannot host & access to your home server at all.

The Vpn u mentioned is commercial vpn which is no problem connecting at all even with private/public ip.