Use a filter menu with the fields being used as a table columns

You can't filter tables by connected records, if this option will be implemented we have solved 2 problems with one solution.

I agree this would be a useful feature. To get around this limitation on the table view, I use a "Search" view. Unfortunately, this doesn't utilize the "filter menu" available under tables, but it does allow you to show (and export) a table of data that can be generated from fields in related objects (tables). But maybe you already know this.