On guitars, the saddle (the guitar version of the koma) is angled to deal with the the different gauge strings needing slightly longer lengths to have correct intonation with the frets. (It gets a bit more complicated, hence bridge inventions like the Tune-O-Matic with tiny nuts to adjust the exact length of each string.)
OK - the weird part: on guitars, the lower, fatter strings are a bit longer. So, shamisen players who angle the koma the opposite direction are (theoretically) making the intonation worse.
Now, since the shamisen is fretless and intonation is finger placement+muscle memory+ear, there should be no issues of intonation: a player has full control over pitch. Koma angle is just an issue of taste and habit viewed this way.
Regarding sweet spot on the skin, that would change with each pitch, and only hold true for harmonics of a given pitch (look up Chladni’s figures on Youtube for some cool examples). So, angling might indeed find sweet spots for the three strings, as Patricksan suggests. String tension is less for the thinner strings, and so Grantsan finds his koma slipping after he beats on his strings - this also makes sense.
One could get pragmatic and try angling the koma this way and that and listen for differences. Recording the experiments would give hard data; notes could be sonogrammed to explore just what is happening in a more objective way.
Or one could just play and enjoy. But, Joelsan, it is a good observation and an excellent question.