For the life of me I have never understood a pergola. It seems like a total waste to me for the very reasons you cite.

Because people are stupid and manufacturers are smart. It’s all about marketing and merchandising and the “next cool thing”. These are popular because advertising works and people stupidly follow what they hear/read in the ads.

Thanks, @JLeslie and @elbanditoroso. I thought maybe I was missing something.
I also question white kitchens and subway tile backsplashes. Keeping it white would be a nightmare, and who wants all that grout to clean?

White is easy to keep clean. You can use bleach. Although, bleach won’t work on dirty grout that’s different than a white counter.

Some of it is just aesthetics and following the herd, but pergolas aren’t really supposed to be complete structures on their own. They are meant to be a support for climbing plants, hanging flowers, and/or green roofs (which do provide shade and are considerably more attractive). Basically, they are like the frame of a house: not very useful if you stop there, but something to build on.

Thanks, @JeSuisRickSpringfield, that makes sense. I have never seen one actually being used except as a frame over some sort of picnic table, but as a way of hanging plants I can see that that would be useful.

I always imagine grape vines on those things. According to Google translate, pergola means arbor in Italian. An arbor is a “leafy, shaded recess formed by trees, shrubs, etc.” (dictionary.com) So I’d say the purpose of those things is to hold greenery.

People often use the term pergola incorrectly here (in Australia). A pergola, as has been discussed, doesn’t have a specific covering. Instead as @JeSuisRickSpringfield said, plants are grown up and over the structure and the living plants provide the shade.

I think they’re much less popular here than they were in the past. Most people would go for a patio cover these days where there is actually a roof to the structure.

Pergolas are functional and look great if they are covered in vines. In the summer the leaves provide shade. In the winter they fall off leaving a bare skeleton that does not need to support heavy snow loading.
Unfortunately it takes a long time to establish serious vines. Most people, Including me, don’t have the patience.
I put a nice arbor in my garden about 10 years ago and planted clematis vines at the base. Now that the vines are starting to look good the arbor is falling apart. You can’t win.