In case anyone is still reading this. (why marker on 10 and not 9).
The most likely reason is not related to harmonics, which is one of the main reasons why instruments use markers.
I propose the answer is simpler. The primary positioning of markers is related to spatial memory and how to jump around the fretboard between notes.
Here is an image of the ukulele neck showing the jumps between finger postions for root notes on all strings.
(GCEA, ADF#B and DGBE tunings all have the same shape (unlike on the Guitar where tunings can vary widely))
I have drawn the fretboard on both sides and the line that connects each subsequent note down(up) the fretboard. In my diagram its on the A string.
The first "+1 Root" diagram indicates how to navigate down to the next occurence of the same note if you are on a note on a string. Follow the line
E.g. to get from any note on the 4th string(in this case G) - go down 3 frets and across 2 strings.
The "+2 Root" diagram shows you how to jump down two notes. You can see how the +5 and +7 distances are critical.
You can use the visual references of the fretboard markers to spatially move from where you are now, down +5 or +7.
The "+3 Root" jump shows that +10 is the distance for the 4th(G) string. Its as far as you jump in one octave. Of course the +1 loops into the next octave from here.
Try this method to play all over the fretboard instead of just at the top. Of course you'll need to adjust your fingering to the shape for that string and chord. For diagrams on all of this check out
https://ukulelethoughts.blogspot.co.nz/
I contend there is no good reason to stay with only a few memorised chords when you need to remember only a few specific spatial shapes and offsets to play all notes anywhere on the neck...