Prove your uptime, do not just claim it
If you publish an SLA, at some point a customer will dispute a month. When that happens, availability data measured by your own infrastructure is not persuasive — it is the defendant testifying on its own behalf.
Third-party monitoring from outside your network gives you an independent record. It also protects you in the other direction: it lets you demonstrate that an incident a customer experienced was on their side, not yours.
Watch the auth path separately
Authentication tends to be the most heavily depended-upon service and the one most likely to fail in ways that are invisible to a health check. Token signing keys rotate. Session stores fill up. Identity provider integrations expire.
Monitor an actual login round trip against a synthetic account, not just whether the login page renders. The page rendering proves your frontend is alive; completing a login proves the system works.
Regional failures hit specific customers
A SaaS product with international customers will eventually have a regional problem: a CDN edge serving stale assets in one metro, a routing change that black-holes one country, a cloud zone degrading.
From a single monitoring location, all of these look perfectly healthy — while an entire customer segment cannot work. Checking from several continents is what surfaces them before the support tickets do.