Is western culture completely incompatible with daily life? I disagree with your assessment of western culture not valuing productive jobs. If, by "western culture," you mean "artwork and similar media," you might have an argument there, as that is a common theme in a good amount of art we see. However, if you use "western culture" in a broader sense, in the sense that includes more than art, but the lifestyles and ideals of the society, I think the opposite is true. There is an extreme amount of social pressure to do something "productive" in society; usually, this is because "productive" fields are in higher demand than "unproductive" fields, so they pay better and are seen as more financially stable, thus making them "smart" choices. Tell people you are going for a degree to become a doctor, engineer, lawyer, businessperson, corporate scientist, or similar job and expect a lot of smiles and follow up questions about particulars (what do you want to with that). Tell people you are going for a degree to become an artist, philosopher, sociologist, or something similar and watch as polite people's eyes slightly unfocus as they try to think of a way to carry on the conversation, while not so polite people ask questions like "what are you going to do with that?"
Even how we talk to each other reveals how much we value work and what you do. When meeting someone new, one of the first questions you ask them is some permutation of "what do you do for a living?" I would not be surprised if it is the next one most people say after "what is your name?" Most of the art produced that champions the "unproductive" fields and aspects of life is a reflection of western culture's job-focused obsession. It resonates with people particularly because they feel their jobs are oppressive and boring. The artist is seen as free and above the concerns of this job cycle, doing what they want to do, much like the viewer of a story about an artist struggling to make it and eventually succeeding wishes they could do. Think of the movie "Office Space." The conclusion and final speech of the movie is that practically no one likes their job, so you find something you can tolerate and go from there. Do you think the majority of people working right now enjoy their jobs or even get any type of fulfillment other than the money and social status that comes with it?
The reason we do not talk about "productive" topics to be consistent (whatever that means) is for a multitude of reasons. First, work is draining. We already spend a vast majority of our time doing things we do not really want to, so why would anyone want to spend their free time doing work outside of work if they do not have to? Second, as mentioned, these topics tend to be uninteresting, so talking about them with most people will not be socially productive. Third, a lot of topics that are important to discuss can turn into a can of worms. Talking about anything related to politics, philosophy, religion, economics, and such can turn nice talk into anything ranging from awkward to angry. You learn not talk to anyone about these topics rather quickly. Fourth, people probably do not have knowledge on the topics, so discussions tend to exclude one or both of the parties. I love philosophy, but there are topics I do not know about, so when people talk about these topics, I do not have anything to discuss, so I avoid these discussions. Lastly, and this is most important, pragmatically, I do not see how people with no real working knowledge of a subject discussing and working on the subject aids in its progress. For example, robotics may be important, but most people have no idea on how AI works, let alone on a level required to talk about robotics. At best, you have people talking about weird hypothetical scenarios with no pragmatic basis. At worst, you get people who think they know how to progress, but have no idea how nonsensical their ideas really are.