Actually scheduled filters for Smart Lists came out later. Initially Day/Week/Month views were the only option to filter by dates.
Since now there is scheduled filters on the lists, you may see the ones you like on list view. But on day/week/month views, it'll filter only the tasks that's available on list view.
You may use 'All Lists' or other filtered lists to simply use 'Day' view as 'Today'.
Using 'Day' view will show you tasks including overdue ones on today's date for every lists. (Setting 'Overdue tasks on' should be set to 'Current date'. It's set by default)
This will let you see week/month views with tasks on that date as well.
While using 'Scheduled Smart List', I recommend using 'Within 1 day' to get today's list with overdue included. It's same as the one you've set but having less filters will increase performance. (You may not see the difference but anyway ) Using this compared to day view would be simplifying and having dedicated list to be focused on it.