Indeed. It's one of my favorite films as well, and consider that I'm a PKD fan: I don't think it's even a companion piece to the book. It hits some of the same themes, but Blade Runner is more neo-noir with smoke-filled rooms, and Do Androids is more PKD exploration of ideas, religion, anxieties, etc. PKD loved what he managed to see of the movie before dying, mind you.
I think what makes Blade Runner engaging is that it's not trying to be a direct translation of the book. It even reverses some of the book's characterizations: "Rachael" is in the book manipulative and a liar, but in the movie she's naive and the one being lied to. The androids from the book are cold and callous, almost completely unempathetic even for their own kind. The replicants from the movie are way more empathic -- Roy Batty is arguably an antihero rather than a villain. I've watched Blade Runner many times, being one of my favorites, and there are times I consider Roy the true protagonist of the movie.
It does hit some of the same themes of PKD's works: what is real and what is fake? What is human, and what deserves to live?
Sometime it takes a while to grasp the significance of a poem.
Yet, after recently re-reading Do Androids Dream of Electric Sheep? I came away thinking that the movie could have been so much better. They left a lot of the interesting details and Phillip K. Dick weirdness out.