I think the answer depends on the objective:
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If you are looking to distribute a library that is intended to be integrated with other software wrapping it in Docker will make it hard if not impossible. Here building a pypi or conda package makes more sense (although I do not know how are you going to deal with the Java dependency - but do you still need JVM after compilation using JCC?).
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If you are looking to distribute a command line tool with complex set of dependencies Docker is a good fit.
In other words distributing nilearn in Docker makes little sense, but distributing FMRIPREP in Docker makes more sense.
To answer your other questions:
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There is no data on what percentage of neuroimagers know how to use Docker. There is however a growing list of publications and training materials that use Docker in context of neuroimaging.
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Docker is slightly slower than bare metal on Windows and Mac, but runs as fast as native on Linux.