At some level this strikes at the heart of the question 'what is a post-doc good for'. I manage a research group at a national lab. So, I hire post-docs, and I hire staff members (physics, materials science, chemical engineering, related fields). What value proposition do I tell the new post-docs, and why do I value post-doc experience for staff hires?
For the new post-docs, the story goes something like this. You just spent 5+ years doing a PhD. In the process, you learned how to do research, and did enough of it to have a body of work suitable to receive a PhD. Congratulations! Now you get to do it again. And again. And on a short time line.
A successful post-doc will pick up a project, and have presentable/publishable results in 6 months or less. (Note that my strong preference is that the first project will not be intimately related to their dissertation work.) They will then add another project, and again be productive on the second one within 6 months or less, while continuing with the first. By 18 months they will have multiple results, over multiple projects, and be able to give a great interview talk solely on their post-doc work. So, they must show that they can get involved in something, come up to speed quickly, and have impact on multiple on-going projects. Post-docs from the group have gone on to have successful careers at national labs, industry, as well as academia coming out of my group.
For staff hires, I strongly value somebody with a post-doc background that shows this. Why? Well, guess what - over the next 30+ years you will not continue to do what you did in your PhD research. Being able to show that your PhD was not a fluke and that you have the skills and desire to keep learning new things and be productive in new areas is a great story to tell. For industrial R&D positions this has resonated quite well with the hiring managers that I've talked to (had people hired by) - it really reduces the perceived risk for the hire. Similarly, for national lab hires (internal or external) it again makes a great story - staff that can move rapidly in new directions are very valuable. If the post-doc is aiming for academia, I will make more of an attempt for the various projects to more clearly related into one 'bundle' that would be a visible area of research interest and grant funding opportunity. Still, the principle applies - you show that you truly are capable and talented.
How important is it for you? I can't say. The more applied an industrial position is, likely the less that they would value the post-doc experience, even in the hiring process. They may even devalue it since you would be too 'research-y' for them. But I would maintain that even there, being able to tell a clear story demonstrating that you have the skills to jump on to a project and be productive very quickly should be appealing to them. Now, if they will hire you directly out of grad school, than there isn't much value to the post-doc. If you want the industry job, take it. But realize that you will be expected, and should be able to talk about in the interview, your abilities to jump in to something and make it work.