This question reminded me to ask what is the origin of the special trop for the masa'ot - the section enumerating the places Bnai Yisroel travelled, as described in B'midbar 33:10-49. A recording of the leining can be heard here starting at 5:53.
This question has also bothered me for a while. A search of Otzar HaHochma led me to the Nitei Gavriel Hilchos Bein Hametzarim, Vol. 1 page 154 who brings differing customs and cites the source "this is what people do (kein ama dabar)." He then quotes the sefer Shaul Bachir quoting from the Maharam Shick that the different customs depend upon whether the travels were a source of pride (Ramban) or shame (Rashi). A thought of my own: There is also a custom not to stop in the middle of these pesukim. I wonder whether the custom may have developed to remind the baal korei to keep going.
R. Tzvi hirsch Weinreb writes in The Person in the Parsha pp497-498(I have excerpted):
Immediately after the long list of brief stops on the painful journey, at the conclusion of all that travail, God says to Moses...when you pass over the Jordan...you shall drive out the inhabitants...you shall inherit the land by lots..."
Aimless wandering with no end in sight is torture; a journey with a clear destination, on the other hand, is a wondrous experience, despite its many obstacles. Without the promise of the inheritance, ...the many way stations would be chanted to a very solemn melody, perhaps even to the melody of Lamentations...But with the vision promised to us...all of the sufferring along the way becomes worthwhile.
The lengthy list of way stations becomes transformed into the lyrics of a triumphant marching song