Is accreditation of a tool necessary or required?
For an estimate of your carbon footprint, accreditation is not necessary.
For tools that provide formal reporting to customers, government and other stakeholders, accreditation is desirable. The question is who does the accreditation and what it entails. Any organization can say that they provide an accreditation, but if there is no standard attached, and no independent supervision of the process, then that statement has little value.