do you think its absolutely necessary to paint the interior doors?
No, unless they are in really bad shape then I think it would be a waste of money. Presumably all the interior doors will be wide open (do leave them wide open as it gives a much better sense of space than doors that are just ajar) so nobody will be looking at them "face on" as it were.
I also think you are very wise to allow buyers to open all cupboards and wardrobes, everybody wants to see how much storage there is and if some is closed off to them they might suspect something off, like a wall protrusion necessitating a shallow wardrobe, or part of the wardrobe being unuseable or, possibly worst of all, damp.