tl;dr: Network Administration 101. SSH is an application-layer protocol. Just because it provides an 'easy' path to encrypted remote filesystem access doesn't mean it's a one-size-fits-all solution.
Just because *nix hosts treat everything as a file doesn't mean all networking can be handled via remote filesystem access (ex windows hosts, network hardware, etc).
SSH is an application-layer protocol. VPN provides access at multiple layers of the networking stack depending on the protocol used (ex PPTP, L2TP).
For instance, if you need to remotely activate all the machines on a remote network for maintenance. A simple approach is to broadcast a WOL (Wake-On-Lan) packet to the remote subnet. Due to WOL being a Layer 2 protocol, this is not possible using SSH alone.
Same goes for remote monitoring the status/health of a remote network via SNMP traps (also Layer 2).
Remote router/switch configuration, packet analysis, and many other lower level administration tasks require access to the lower layers of the network stack. All of which can be accomplished over a VPN but not SSH.
As for the reasoning behind using HTTPS, see my other comment. SSH access should only be granted to 'trusted' clients and it's usually a good idea to disable it when a 'safe' alternative is available.