Please rate the improvement of saving the filter Show open/closed/all at the BP level

I would be happy to give an assessment if I fully understood what to assess.
Please provide a more detailed description of the required functionality using an example.

The filter has a parameter Show open/closed/all, it is necessary that the selected option is saved for the Business Process in which this filter was installed. Completely by analogy with saving the display or hiding the filter itself.
For example, I went to the Orders BP group, set the filter to Show only open, went to the Tasks BP, set the filter to Show all, now when I go to these BP groups, the filter always has the previously selected parameters.
As I understand it, they will be saved in cookies.