The greek letter mu IS the micro sign, where do you think it comes from?
MICRO SIGN (U+00B5)[1] vs. GREEK SMALL LETTER MU (U+03BC)[2]
1: https://www.fileformat.info/info/unicode/char/00b5/index.htm
2: https://www.fileformat.info/info/unicode/char/03bc/index.htm
I’m not a font designer but I can imagine that the micro sign often appears around Latin letters whereas the Greek letter mu doesn’t, so that font designers might space them differently for that reason.
For fun I compared 10µm (upper; using the micro sign) with 10μm (lower; using the greek letter mu) in the comic sans font face. https://imgur.com/qwnnAqD
IIRC, to enable adoption. Many of the codepoints were adopted from other encoding systems, and it was often useful to support 2-way conversions without loss while Unicode was being adopted.
What's a "duplicate" is also sometimes in the eye of the beholder.