As to why; well, to my mind at least, adding a compass to a travel Uke kind of underlines the purpose of that Uke and differentiates it from other or ordinary Ukes. I have a well worn Uke that’s for outdoor use and traveling, I’ve a mind to add a compass to it.
I looked at your comment about compasses reading incorrectly next to metal and thought it correct, but as ever things ain’t that simple. Taking a button compass (mine’s 20 mm in diameter) I found magnetic north and then placed the compass next to my steel music, as expected the compass found the stand more attracting than magnetic north and hence gave a false reading :-( . I then placed the same compass on my Soprano’s headstock, centrally between all the tuners, the lower amount of metal in the tuners (compared to the stand) gave minimal if any distortion of the compass reading: as I horizontally rotated the headstock the compass dial rotated to point towards magnetic north. That’s just what I found, but YMMV.