Ssh – Automatically spawn a ControlMaster background process on first access to a ssh remote system

Lately I'm often using the SSH client's ControlMaster feature, which allows me to use a single SSH-TCP-connection for multiple shells and port forwardings to the same remote system. The most annoying thing about this is, that the first shell's process that is opened becomes automatically the ControlMaster. That means, if this process gets terminated, all other shells and port forwardings using the control master connection become unavailable.

I would really like when the first ssh command to a remote system would spawn an additional background process which holds the connection as long as there are still connections using the ControlMaster connection, so I could simply close the actual shells whithout having to risk to crash other connections. Ideally the background ControlMaster process would even be configurable to wait for an amount of time for new shells or port forwardings to use the ControlMaster before finally shutting down.

Is there a way to make the ssh client do such a thing? I know I could create such a connection manually before using ssh to create the first shell, but I explicitly want this to happen automatically because otherwise I would surely forget to do it every now and then.

Letting a wrapper script do it also wouldn't be so easy because I often use configured shorthands for remote server names in .ssh/config and the ControlMaster socket is created using USERNAME@NETWORK_NAME:NETWORK_PORT as name. So a wrapper would need to understand .config/ssh perfectly to work as intended.