Definitely this sort of homework needs doing, but it doesn't need to be done by a manager. The underlings can (and should) do all of this research and feed their findings up, and that's when the manager should get involved.
A coder might report "There's an off-the-shelf module we can use that will save us about 20 hours of coding time, but it doesn't handle X in quite the way we need and we won't have access to an API to extend it if our needs grow". The manager should then apply their greater high-level understanding of the project (for example knowing things like time is more important than money on this project) and their domain knowledge (knowing what an API is, understanding the risk of not having source code etc) and come up with a decision.
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