Project Manager's Responsibilities

A friend in a software company complained that the company's project often gets out of control and the customer's opinion is very high. since I am in charge of PMO (Project Management Office) in a software foreign company, he expects me to recommend some project managers with the following responsibilities:
1) lead the project team and develop a work plan;
2) requirement analysis;
3) Database Design
4) system design;
5) build the technical framework of the system, and solve technical difficulties and compile the core Code ...
The above requirements are also misunderstandings of many software enterprises in China regarding the responsibilities of software project managers: they are both proficient in software development technology and familiar with software project management. I told my friends that this requirement is only suitable for the technical director, but the technical director often cannot solve the problem of Project Runaway.
Based on years of project management and PMO management experience, I think the responsibilities of the project manager should be:
1) identify project requirements and properly manage customer expectations;
2) develop a project management plan: Clarify the project objectives, scope, project organization structure, software process model (waterfall/RUP/prototype), milestones, and detailed progress plan, change/risk/communication/progress/quality/configuration and other management methods;
3) control the project, balance the conflicts in the scope, progress, quality, and cost of the project;
4) obtain the customer's acceptance and end the project;
All in all, the most important thing for a project manager is to be familiar with the process management of software projects as long as they understand software technology.
In fact, I have met a project: I have been working for two years, and I am always at a loss. The customer feels very tired and almost intends to give up the project. The project manager works very hard, the customer also recognizes the capabilities of this project manager. At that time, the CEO handed over the spam project to me, who had just entered the company. I found that this project manager is a technical madman: a project manager, a technical architect, a demand analyst, a system designer, and a developer of the core module. The system is very beautiful, however, it is far different from the customer's business requirements. I remember taking the following measures:
1) Designate a project manager responsible for project process management and requirements;
2) re-assess the requirements and re-plan the entire project;
Through my efforts with the new project manager, I accurately grasped the customer's expectations and re-established customer confidence. In those years, this project became the company's most profitable project.