The ability to to have the information displayed and on the go with the App is great for us as we can engage with stakeholders and its bought in consistency for out out of hours team on alerting.
Integration with CloudWatch, webhooks, Jira is outstanding, functional, and reliable. The application has gotten better over the years I have used it.
Love the on-call rota, the ability to schedule overrides and multiple call out hierarchies. The wide range of alerts and abilities to interact with the product via multiple channels.
We also suffer during outages for the lack of a "acknowledge all incoming pages" button.
Once I actually closed an incident of another person, mistakenly. Yes it was my mistake and perhaps my IT department's configuration mistake, but the UI shows me these incidents.
We badly need a "current status, open incident" that auto-acks whatever comes in and, say, converts them to summary push-notifications or some other "just an FYI, this other stuff happened" digest.