It's common practice for small players but Amazon, Microsoft Azure and Google Cloud host their status pages on their own servers because they value the marketing aspect higher than a functioning status page for their customers.
No matter how much you value science and engineering, it ultimately doesn't matter to the business unless that aligns directly with their revenue stream. Sometimes it does, sometimes it doesn't.
So I don't really understand what they gain by doing it. I think maybe I am wrong about it being a marketing concern and that the choice is more related to internal politics and incompetent management.
Few companies really respect their engineering teams/divisions in any sensible form from my experience, though I'm biased (even in heavy R&D environments). You're simply a means to an ends.
I understand your point though (and identify with it), but I find any mechanism/option that provides a way of containing potentially damaging information is going to be pushed by management over the option to release damaging information that a responsible engineer may want to disclose.
You're in a culture where admitting fault or liability is like pulling teeth and ripping finger nails off. It shouldn't be IMHO (we should own up to our mistakes and be reasonably forgiven), but that's unfortunately not the culture we have.
If they self-host it, it signals that they're overconfident in their ability to maintain an accurate status page.
Given these two options, which do you think a budget manager will have an easier time signing off on and defending upward?
When you're advertising uptime/availability, you're motivated not to report downtime/unavailability. Then the value of such reports is lost; developers start banging their heads trying to figure out if it's a service outage or a bug in their software (yes, informed by personal experience).