At the moment you have for each entity a Quick Find functionality (Web client) and a related view called Quick Find. If you enter a search term into the Quick Find Box, you get the result shown in the view "Quick Find". This view have a default filter (Standard: Status = Active). In some cases this default filter is good, but in some cases you want to search inside other filter definitions, like Status = Inactive. Therefore you can customize the Quick Find View inside the Customizations. But now you can only use the Quick Find to serach inactive records. You have no chance to switch this filter without customizations. But we need it more dynamic, without customizations.
It will be better if you can choose a entity view first (f.e. "Inactive Accounts", Filter: "Status" = "Inactive") and after you enter a search term into the quick find box, then you get a result found in your selected view (in this case: inactive Accounts). If you change the entity view (f.e. into "Active Accounts", Filter: "Status" = "Active") an use the same search term you get a different result as before (in this case: Active Accounts).

So the requirement calls: The Quick Find functionality works in context a selected view for each entity.