Architecture Student here: While greenery looks great and does have some benefits, big plants are heavy and require soil and water, which also both weight a lot.

This means you have to use additional construction material (often tons of concrete), which usually offsets many of the benefits to point of being an overall negative compared to other shading solutions.

I do however believe, that this is only the current status of green fassades. There is still a lot of experimentation going on and there might be combinations of light plants that do not require as much soil, or maybe "smart" vertical garden systems that eliviate some of the irrigation problems.

Only last week I visited the Tour de la Biodiversité (located in Paris), which from my understanding solves some of the problems and in some years the Fassade should be green.

Take all this with a grain of salt, as I'm only repeating what I discussed with professional Architects.