I think the question can be extended to cover test automation frameworks in general, doesn’t have to be just for API (testing).
It would probably have to be a compromise between personal preferences + team/company fit + management expertise with the chosen technology down the line based on hiring from market & existing team/company expertise.
Personally, having done such evaluation/research some time back, I would much prefer not to build a framework from scratch and use an existing general purpose framework for the job and customize it for one’s organization’s needs.
My personal preference would be to use RobotFramework where possible, for all its general purpose feature set & it’s ability to work cross programming/scripting language by way of remote interface for test libraries, allowing one to code test tooling for the framework in other languages besides python & Java. There are not that many frameworks out there that have cross language support.