It depends on how good the service is. In my experience, the service experience is usually something like:

1. Alert is created due to something in the SaaS not working

2. On-call engineer is pinged

3. On-call engineer creates an issue with the SaaS provider

4. On-call engineer twiddles their thumbs waiting for an update from the SaaS provider

I've been that on-call engineer dozens of times. I'd rather be able to have some kind of agency when triaging an issue.