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It seems to me that attributes for "id", "startTime", and "endTime" should be added to the VTTCue interface in section 7.1 of the January 2015 draft. The last two are parameters in the constructor. The identifier "id" is described elsewhere in the document and the attribute "id" is already allowed by several browsers. "id" could also be added as an optional parameter in the constructor. As a convenience to programmers using the VTTCue interface in applications, it would be useful to have way (possibly a function) for adding a WebVTT cue settings list to the cue as a single string using the same format that one would use in the WebVTT file on the start and end times lines. This string could also possibly be added as an optional parameter for the constructor.
VTTCue extends TextTrackCue: > interface VTTCue : TextTrackCue Which is defined here: https://html.spec.whatwg.org/#texttrackcue interface TextTrackCue : EventTarget { readonly attribute TextTrack? track; attribute DOMString id; attribute double startTime; attribute double endTime; attribute boolean pauseOnExit; attribute EventHandler onenter; attribute EventHandler onexit; }; So id, startTime and endTime are already part of it.
As Brendan explained in comment#1, VTTCue extends TextTrackCue, so all the attributes that you're missing are actually there.