Most outages are found by the wrong person. A customer emails, a client rings, someone posts in a channel you were not watching. By then the question is no longer whether the site was down; it is how long it was down and why nobody noticed.
A scheduled check from outside your network answers that continuously and keeps the record. When a site fails, the run holds the response it gave and the location that saw it, so the conversation starts from evidence rather than from someone's memory of a screenshot.
It also catches the outage that is invisible from your desk: the site that is fine from your office and unreachable from the continent your customers are actually on.