Some font-families might want these letters to look different for some reason. Even if they look the same perhaps the boldfaced or italics should behave differently, perhaps the spacing should be different etc.
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
> Why would they deliberately put duplicates in unicode though?
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.