To me, the key difference between shooting with a review screen and shooting without one is that a review screen lets me evaluate the image while I'm in the field. That sounds good--and for shooters who have only one opportunity to get it right, it can be indispensable--but for my style of art/hobby photography, being able to review the screen means that the camera starts competing with the subject in terms of visual interest. Not having a review screen means that, if you want to look at something interesting, you have to look at the subject. This encourages me to spend more time finding ways to conceive of and capture the subject. On the other hand, the review screen encourages me to make a technically perfect capture--exposure, focus, stability are all spot on. But technical quality is meaningless when the scene is poorly composed, and I feel like I'm more likely to compose well if I'm not distracted by reviewing the images I've already taken.
My ideal camera would drop the rear screen in favor of a phone interface. The camera would be thinner, lighter, and have longer battery life; it would have fewer points of failure; it would also have fewer things to distract me from shooting, which is what I use a camera for. The phone/tablet would have a higher quality screen and probably a better interface for reviewing images, but would be entirely secondary and unnecessary during the shooting process.
Cheers,
Jon