Tenting isn't really encouraged on any Camino route. I've never actually seen any kind of campground on any Camino route.
I do come across people tenting, but they are in most cases pitching their tent without permission in most cases and camping rough.
Kind of a grim way to save on accommodation cost.
I'd certainly miss a shower at the days end!
On the Camino Francés or not that far off route are ~ 20 official campsites. Cost is roughly the same as albergues and include shower ect. Plus some albergues that allow camping in their gardens, at same cost as a bed or slightly less, with access to shower and kitchen.
When you don't camp, it is easy to overlook that of course.
For me on the Francés it wasn't about saving money, but because I love sleeping in my tent (in France and Germany it does save a lot of money, though, since cost for accommodation is much higher there).
Anyway, I camped on many occasions on the Camino (Francés, podiensis, Germany, Cluny way...) and certainly would bring the tent again.
On the via podiensis, during camping season, you can camp every single night, legally, on an official campground or in gite gardens, if you want to (=with shower ect).
Camping legally like that is not "rough" at all. Sleep in your own little home listening to crickets and birds, have a good meal in the gite or a restaurant from time to time, have a nice shower, then go swimming in the campground's pool (the bigger ones often had a pool and/or a restaurant). I found that quite luxurious.
But in winter most official campsites will be closed, in Spain as well as in France, and probably also many albergues/gites that allow camping.
So it makes more sense to bring a tent in summer, and even then only if you really love camping, not as a "just in case".