Thank you for your interest in TeamPulse and sharing your ideas and requests.
You are right that in the current implementation all Tracking screens (My Perspective, My Task Board, Story Board, Task Board and Progress Grid) do not support saving of custom view settings. This was mainly done, because we consider those screens views of the current iteration and we believe that current items should be tracked there even when the last time you opened the screen you checked the previous iteration for example.
Most of the other screens support preserving current and saving and applying shared views. On all those screens you are able to select the Initial View (check attached screenshot) which will update all filters and grid settings to the default ones. There is also global reset settings button (check attached screenshot) that will reset settings on all screens - this means that on all screens initial view will be selected (all custom views will be lost, however all saved views will remain available for use).
Here is a link to our documentation where you can read more about using shared views.
In order to help you define that current filters on each screen there are orange icons that indicate is filtering is applied. Next to the page title you will see an icon if any filter is applied with a tooltip of a list with all applied filters (check attached screenshot).
If you still feel that shared views should be added for all screens in TeamPulse, please visit our Ideas & Feedback Portal and post a request. The more votes an item gets - the higher priority it will get in our product backlog.
the Telerik team