Hm, I'd say I've folded several tessellations, but I went for the "true love" option. In the end, I think you can "even" love tessellations without ever having folded one.
And while I do like representational folds, I am also fascinated by tessellations. To me, they are pleasing to look at - can a pattern not be art enough?
My partner doesn't quite see it like me, though. He always asks me what I'm going to make with the tessellation. For him tessellations only seem to be a technique for enhancing representational models, e.g. for adding scales and such to reptiles or fish. [By the way, he doesn't do origami himself.] I have tried to explain that I love the beauty of the pattern, and that the model is finished - but it's just not for everyone.
Having said that, I do think that tessellations can enhance representational models. Think of Robert Lang's Koi or Kamiya-san's Ryu Jin. There are of course many other examples, but those are the two most impressive I know. And one day, I tell you, I will fold that Koi!
-- Sara