This is hardly a novel problem. All manners of talking, noisemaking, and other disturbances have been problems in theaters for centuries; phones are simply another type of potential disturbance.
Yes, it is to some extent a cultural problem. I also think it tends to be a problem of lack of any enforcement of reasonable etiquette in theaters, perhaps from a concern for repercussions and retribution, but also, at least in many movie theaters, from a lack of staff.
But I think it is only through enforcement by venues, and cultural unacceptability, that disturbances like these can be minimized, especially in this case. I don't think anyone particularly wants to be in a theater full of other people on phones; the people who use them in theaters would likely be upset about others using them were they not using them at that particular time. There are already venues for watching movies on large screens while being able to talk and generally be more casual, and perhaps we could use more of those, but that's not the problem here: the problem are people who are selfish. If someone wants to be able to disturb others, but not be disturbed by others, then letting everyone cause disturbances isn't going to help: everyone will go to the no-tolerance shows, and become upset if they're thrown out.