Thanks for the samples. The piano is a good example (I think) of a photo converted to a b&w version with the threshold filter in an image editor. It is also a good example of when NOT to use svg, in my opinion. The second one would need some manual cleanup as a vector, i.e. a complete redraw, in a vector illustration application. It could be worthwhile as a svg.
But honestly, with Color Quantizer the piano goes down to 33.9 kb (original size 68.2kb), while the second sample results in 4.28kb (versus 9.41kb gif).
Still 50% less - which means 50% less bandwidth, and your page loads faster. Granted, does not look like much, but when all the graphics in a website are optimized like this, it means less bandwidth costs, a faster browsing experience for your users, less processing power, less stress on the environment (and the user), and you save the world!
Well, perhaps not. :-)
If you are on a mac, try out https://imageoptim.com/command-line.html
For a nice comparison chart, visit http://jamiemason.github.io/ImageOptim-CLI/