Analyze the theoretical challenges and benefits associated with implementing a comprehensive smart city infrastructure in a densely populated metropolitan area. Focus on the integration of advanced technologies such as Internet of Things $($IoT$)$ devices, artificial intelligence, and big data analytics into existing urban systems. Discuss how these technologies could optimize urban operations, improve quality of life, and enhance sustainability, while also considering potential obstacles such as cybersecurity threats, data privacy concerns, and the need for substantial financial investments.