To borrow your joke, please transform "homeomorphic endofunctors mapping submanifolds of a Hilbert space" into plain language with no loss of precision.
On one hand, writing that into plain language would take forever. By the time I'm done, I would have probably written a small book on algebra. Here, the use of jargon is definitely precise. If you wanted to present this in a topology conference, where it might be important that the number of dimensions of the space is infinite, it would be probably a good start.
On the other hand, thousands of people use git everyday without understanding a single word of this description. But if I say instead "git is a distributed version-control system for tracking changes in source code during software development", my clarity has now skyrocketed. I definitely lost a lot of precision, but my readers will still be able to replicate my results.
That's not to say that there is no necessary jargon - my own definition uses "distributed version-control", which is absolutely key for understanding what's going on.
A paper is not source code - it is a tool for scientists to share their discoveries with fellow humans, and fellow humans will always appreciate clearly expressed ideas. After all, what good is a tool for knowledge sharing that's accessible only to a few? Now, I've argued before that some papers are necessarily difficult (because the topic is very specialized) and I stand by it. At the same time I do think a good paper should attempt to reach as wider an audience as possible, and jargon goes against this concept. I think the joke that "Git gets easier once you get the basic idea that branches are homeomorphic endofunctors mapping submanifolds of a Hilbert space" illustrates this concept beautifully.
For non-toy examples, there are notes freely available on Donald Knuth's "Mathematical Writing" course [1]. These notes are a must read for scientist, and they include several examples of how replacing jargon with plain English can do wonders to improve readability. Page 7, in particular, explains how to rewrite a proof that "is mathematically correct (except for a minor slip) but stylistically atrocious".
[1] http://jmlr.csail.mit.edu/reviewing-papers/knuth_mathematica...