The DTA’s Performance Dashboard seems to be the closest thing I have found that tracks user experience related performance and displays the information publicly.
As stated on the website:
The Performance Dashboard makes data open and accessible by measuring
the performance of Australian government services against the Digital
This promotes government transparency and helps drive the ongoing
improvement of government services — for all Australians.
And you can see a snapshot of the information presented, and the KPIs that are measured:
- User satisfaction – The overall satisfaction rate with the service.
- Cost per transaction – The estimated cost to government, per transaction, for administering the service.
- Digital take-up – The adoption rate for the digital service.
- Completion rate – The overall rate of completion for users of the service.