The ability to connect a quick filter on a Dashboard to any, or all, of the Dashboard's Worksheets is a huge big deal.
Not being able to do exactly this has been one of Tableau's most glaring design gaps for a long time. The lack of this functionality has led to all sorts of workarounds and tricks, all of which have had to their own problems, direct and indirect.
The big fly in the ointment is that although it's really handy to know from which Worksheet an given quick filter came from, this valuable piece of information isn't put front and center. In order to find it, one has to navigate three levels down into the quick filter's context menu. This isn't a bad place for this information to be presented, but it's really ungood that one needs to dig down there to find it.
Not providing relevant, valuable information in the primary context, where it's available without the User needing to dig around for it.
Tableau's value is in it's ability to provide easy, transparent access to the information in business data. It should take and zealously enforce the same guiding principle with its own information; in this case it doesn't.
This Tableau Public published workbook's dashboards demonstrate the situation.