1st phase of requirement analysis : Problems faced by Project Manager

Project manger is not able to identify the customer's need, as customers don't know what they really want.

As customers is not clear of  what they need, and it's up to you to ask the right questions and perform the analysis necessary to turn this lacking vision into a formally-documented software.

Accepting the unreasonable timelines of the customer and jumping into the project without performing a detailed analysis and understanding both of the scope of the project and the resources necessary to execute it.

Customers have unreasonable timelines is one of the problem faced by Project Manger, by which the project will either get delayed or suffer from quality defect.

The purpose of the requirements phase is to specify the functionality of the proposed system; therefore the project manager  should concentrate on the completeness of the specifications. The decision to purchase a package from a vendor would come after the requirements have been completed.

Customers want to involve vendors as they are either starting a new idea or changing an existing idea.
In the first case, if it is a new idea, the customer is also learning and explaining what is required so the business analyst is to ensure that he/she factors this in the discussion with the customer and does not finalize the requirements till there is a common agreement with all the stakeholders. Also the BA is to ensure that enough budget, schedule is factored to incorporate the changes that the customer would ask for once the requirements are frozen.
In the second case where it is the change of an existing idea – note that usually the people who impart the knowledge of the existing system are veterans or SMEs of that system – who are handing over their ‘baby’ to the vendor. In many cases, these SMEs would be asked to move on to other roles or organization once this Knowledge Transfer is done. So, the BA/Requirement Manager is to factor these issues and delays and see if all the meetings are agreed upon well in advance and there is a team in place to do quick POC/documentation that can be validated by these SMEs and other stakeholders.
In both the cases, the BA/Requirement manager is to ensure that all the stakeholders are involved and sigh off. Typically this phase would call for a T&M rather than a Fixed Price for the requirement gathering phase. Once the requirements are finalized, then it can move into Fixed Price.

I feel even you do best of the documentation the problem is that the clients are not willing to read them and give you a sign off and freez them