Or might that be due to potential negative brand marketing that springs into existence when users see such a notice inside their application?
When Slack is down, Slack can't tell you when it is down. It's why status pages are often on other domains/systems etc, so the status page remains up while everything else is on fire.
If they have it on an API call to (making it up) api.slack.com/status it might very well go down when things go wrong, making it useless.
However if they physically host it elsewhere ideally on a different cloud provider, with a different domain, say, slackstatus.com/api-status that is completely separate from the actual services, which can both query the actual service with a call from outside and can be updated manually with physical persons at Slack, and the client checks that domain, I think it can work.
It sounds more like laziness than complication to me. But that typifies Slack dev culture—“just use duct tape”
And in an absolute worst-case infra collapse, someone there could manually edit/upload a new one...
/feed subscribe https://status.slack.com/feed/rss