You're so stuck in your line of thinking. How about you run an API and host the client in a native app? Problem solved. How about you don't run sshserver. Problem solved.
For me it's more about security. If I have a an appliance tied to the internet my entire network is susceptible. With an app, and bluetooth, I could just send data between the appliance and the iPhone, and then use the iPhone connection to the network to send data to the server (if needed / wanted but probably not for this application).