One of the most important things I was taught in physics classes back at school was to always convert each operand to the basic SI unit before using it in calculations. That is, always convert km to m. Always convert hours/minutes to seconds. And so on. This for manual calculations - programming is of course even more pedantic about using proper types. So I can't think of any sensible reason not to do this while writing computer programs. Now as it happens, once a veteran of writing computer programs, you also realize that you should pick a unit which is friendly to the computer, not to the programmer. Because each time you re-scale something going from raw data to some human-friendly unit, you risk losing accuracy caused by rounding errors. You should only need one single such conversion to human-friendly formats, and that's before displaying something.

It solves the same problem that any strong typing system solves: Catching errors.

Yes, it's a sound alternative to convert everything to a single system (I would choose SI too), but anything that involves trusting humans to do the same thing right every time is not as reliable as delegating enforcement to a compiler. The problems such libraries solve are problems like the units conversion error that destroyed the Mars Climate Orbiter at a cost of almost $200 million. The question is whether the solution comes at an acceptable cost in developer bandwidth and maintenance.