I disagree with your take. These are VPNs because you are building private overlay tunnels on top of a public Internet underlay. Just because youre not using a VPN to tunnel into a private (e.g. RFC1918) network doesn't mean you haven't established a virtual private network over the Internet.
Also, these are not proxies. A proxy terminates a layer 4/7 connnection from the user, and established its own layer 4/7 connection to the destination, fully man-in-the-middling the connection. When one is using these widely advertised VPN services, there is no layer 4 or 7 proxy^. Rather, the gateway at the VPN PoP is NAT'ing traffic at layer 3.
^IME, many of these services also provide an HTTP or SOCKS proxy, but that's not what a user is using when they have an app on their phone or thick client on the desktop.
Also, these are not proxies. A proxy terminates a layer 4/7 connnection from the user, and established its own layer 4/7 connection to the destination, fully man-in-the-middling the connection. When one is using these widely advertised VPN services, there is no layer 4 or 7 proxy^. Rather, the gateway at the VPN PoP is NAT'ing traffic at layer 3.
^IME, many of these services also provide an HTTP or SOCKS proxy, but that's not what a user is using when they have an app on their phone or thick client on the desktop.