Software requirements are a contract (possibly even in a legal sense) for software. Plenty of good software has been developed without requirements, but for mission-critical or safety-critical systems, software requirements are vital. They form the basis for validation (meets requirements) and verification (is fit for purpose) testing (what is called SIQT in many organizations).
Requirements are often political because they represent an interface between multiple groups of people with different jobs (even if the ultimate goal is the same).
Recommend EARS.