There's an endless debate about the pros and cons of "dynamic linking".
I think it would be best for the JDK to link to system libraries by default, if possible. For a particular JDK image, one can drop a patched libz into a suitable lib directory to override the system one. It should also be relatively easy to build a JDK with a static libz.a. And all the cool kids are building docker images where they control everything. The zlib/info-zip projects don't exhibit a high level of code health, but OOTO they seem quite stable these days.
