The fact of the matter is most people in the United States have a cell phone these days, maybe even more so than house phones. Not allowing them to be used in public would be a pointless exercise in futility, considering the hardships it would take to enforce something like that, alongside of the fact that cell phones are a good way for two people to communicate and keep track of each other across long distances anywhere from one number, versus many numbers with landlines.
Yes cell phones should be allowed in public. There should be a basis of common courtesy when using them but they should be allowed. If they were not allowed then the benefit of having a cell phone would be greatly undermined and many less would be sold in the world.
People spend a lot of time on their phones. While it may be annoying at times, it is almost necessary. Individuals need things like connection with friends/family (for example: where to meet). They also need it for things like where to go for food, gas, or persons house. Without it there would be a lot of confusion and stress.