Good question! I can’t find much about it, but I did find this:

“The border is the decorative bar that also adds support to the towel’s structure, similar to the beams of a roof.” – source

I think they sometimes bunch up because that border shrinks more than the rest of the towel. I hate that!

Usually more expensive towels don’t bunch, but there are many inexpensive ones that don’t either. I hate when it happens. Ironic it is supposed to help with structure. Part of it is not ony decorative, but maybe a sigature for a brand.

Interestingly beach towels don’t usually have a band.

That band is made of mercerized cotton, which is a treated sort of cotton. It annoys me too, as it always shrinks and bunches up, as you say. I will never buy towels with the mercerized band any more, all our recent towel purchases have simply had a chequerboard pattern at the ends in the same cotton. It looks nicer and stays flat