The biggest reason for shooting on film is because...it looks like film.
20 years ago, Red Hat founder Bob Young told a story about branding that bears on this question. He explained that if you offer somebody who has never tasted Ketchup before two samples, one being the most popular brand in America (which enjoys > 80% market share) and the other being any other brand of Ketchup (chosen at random), almost everybody will find both to be equally unpalatable. Yet among people familiar with Ketchup, the majority specifically prefers Heinz. It is now possible to build digital imaging systems (ARRI Alexa, RED Weapon, SONY F65) that are objectively better than film in resolution, dynamic range, noise, etc. But those features do not influence a preference that is based on familiarity.
As Hans Meiser points out, there's been a huge flip from film projection to digital projection in the past 10 years, which means that extraordinary measures are necessary to even screen films these days. So it is newsworthy and remarkable, like a dinosaur actually walking down Main Street, when a movie is released as an actual film.
Film does have the advantage of being an interesting archiving format. It is not perfect, but when properly stored, it has many advantages over naive digital archiving strategies. But I would say that the principle reason for film's continued popularity among the Hollywood Elite is because the current generation of the Elite grew up with film, and that is their favorite brand of Ketchup. The next generation have different preferences, and they will have their say as the older generation ages out.