Have these statues some function beyond pleasing the eye of the passer-by?

If it should perhaps be to celebrate a local legend then your wished-for gallery is under way, witness the Hartlepool Monkey or the Boy with Leaking Boot. The latter has been enthusiastically adopted in Cleethorpes, though that is only one of a number of representations of him worldwide. I am sure many other places have offerings too, Morcambe's Eric, for instance, being a legend of a different kind. There are quite a few in inland places as well.

I wouldn't want to be overrun with little mermaids (I should have the chance, statues of her I mean) but AFAIK this is only one copy on the theme in over 100 years, it doesn't feel excessive to me.