It's a common best practice to isolate the status page onto completely independent infrastructure - to weather any issues that could possibly happen.
Some lengths companies go:
- Different cloud provider (different region, IP ranges, etc.) to protect against an outage of said cloud provider and their network/datacenters.
- Different TLS CA vendor, to protect against outages from expired/no longer trusted CA's (e.g. the mass Symantec detrust).
- Different domain registrars, to protect against clerical issues, expired domains, etc. (it happens)
- Different name servers (e.g. using different TLD) to avoid outages from the TLD's name servers (e.g. issues around .me name servers). This is why AWS Route53 spreads nameservers across many TLD's.
A lot of the big names go to really extreme lengths - although, some of it appears to be them using status page vendors, so the big names get the benefits of the extreme, even if their risk is actually rather low.
TBH, keeping the status page on a separate host is likely good enough for 90% of possible issues. A separate domain gets the last 10%.