The American Constitution does not need to be re-written because it is already a working document. It is divided into parts. The first part is the Constitution and Bill of Rights. The second part is the amendments, which are exactly as they are called, parts of the Constitution that have been amended. To amend is to change. If the majority of citizens want more modern concerns to be addressed in the United States, then it should be altered through amendments.
No, the American Constitution should not be rewritten to include more modern concerns because that is what the Amendment process is set up to cover. The Constitution already has a built in process for being updated, and that is the Amendment process. Nothing new need be added or written to cover this.