Why can I detect an outage before Tech support can?

Correct and I do know this.  If the OP called to report not seeing a home modem from off the Cox network, as a rep, this wouldn't alarm me because I could see the home modem is online and OP is off the Cox network.

However, since OP verified the outage with a Cox-subscribed neighbor, as a rep, I should poke around or inquire with NetOps.  I'm sure Cox is monitoring their networks and NetOps wouldn't immediately notify the Help Desk because they may be fully aware, assessing and troubleshooting.

First, as a Help Desk, you don't set a quota for the number of calls about an outage.  This is insane.  People are paying you for a service but you'd deny their service until you received 3 more calls.  The first call is a heads up but OP had duplicated the outage with a neighbor.  Take some initiative, make inquiries outside the Help Desk and don't wait for other paying customers to complain.

Second, as a rep, if I can see the modem is online, why would I recommend a service call?  Where would the tech go?  The OP is at work.

You were obviously trained to be reactive and to procrastinate.  I was trained to be proactive and to treat people with a problem with some respect.  We different!