If an index is simply partitioned on date the user will often want to run the same set of fields against a different instance of the same set of data. At the moment switching index resets all the field selections. This isn't so helpful 
Would be good if there was a way to offer to preserve the field selection.
Would this requirement go away if you were able to run graph UI against a pre-defined Kibana index-pattern rather than as is done now with a concrete index name?
Kibana index patterns provides for wildcarded index names and a defined set of fields that are expected to be constant across these indices.
Yes pretty much, it should.
Update - the 5.0 alpha 3 release of the elastic stack now includes a graph UI which uses Kibana index patterns for the choice of datasource instead of a single physical index. This means that multiple indices or aliases can now be used.