IMHO it’s enough to send a message into a Slack channel with incident details like the assignee.
As an assignee, if I want a Slack notification for PagerDuty incidents, I would prefer to update my PagerDuty notification settings (eg: a Slack notification prior to a phone call). So the feature can be: add a Slack DM option in the user notification settings if the user has linked his/her Slack account to PagerDuty.
NB: the Slack DM may add a link to the Slack message in the channel in addition to the link to the PagerDuty WebUI.
Hope Niteesh and the PagerDuty team will find my opinion useful.