Obviously it depends on the level of sheltering. The reality is not really as black and white as the OP makes it sound. The highly sheltered Yeshivish style being described seems to mostly be practiced by the creme de la creme of the Yeshivish velt (like probably Lakewood). It’s become pretty standard for yeshiva bochurs to know a certain amount of pop-culture references (too many in my opinion). The no-smart-phones thing didn’t really catch on well in America at all (I wish it had, but it didn’t). A lot of people in the yeshivish world like to pretend to be more out of touch than they really are when you first meet them.
Sheltering from all references to non-Jewish culture (even stuff like Shakespeare and perfectly kid-friendly literature) can make them seem like weird aliens who are new to the planet when they go out into the workforce. Obviously, that will help them not assimilate, but I’m not sure it’s good for their happiness and success.