I guess it depends what I'm trying to debug, but one thing that seems to be missing from your wrapper is quick logfile inspection. Tailing the last n lines of syslog (or something more specific) is often a good starting point when diagnosing problems.

Perhaps something that performs basic connectivity tests might be useful, too -- pinging the router, an external IP (like 8.8.8.8), and a FQDN (like google.com) would be a good quick test of both internal connectivity, external connectivity, and DNS resolver.