"unprintable"
Define unprintable. You have to determine your final presentation method, viewing distance and acceptable print quality. Just because the print company tells you they need their images submitted at 300dpi, that is just a standard number they throw out there. On that note, "DPI" being used as an image size is laughable because DPI refers to Dots of ink Per Inch, which is extremely low. We use "PPI" (Pixels Per Inch). Anyway, that's off topic.
I read a book years ago that showed the difference between two identical images printed on the same page. One of the images was 300ppi, the other was 200ppi. You could not tell a difference, at all. Now, if the page was printed on a museum quality printer, you could probably tell the difference. But only if you were less than a foot away. After I read that book, I started rendering all of my images out at 200ppi. Once I started rendering images out for 24x36" prints, I realized my computer wasn't fast enough to render out the quality of images I was after, so I stepped down to 150ppi. Guess what - NO ONE NOTICED the reduction in print quality.
I rendered an image for a billboard once. The final image I submitted to the print company was something like 50-75ppi. It looked fantastic from my car zipping down the highway.
With so many presentations being made digitally nowadays, I've been rendering out images at 1920x1080. As 4k screens become more common, I'll probably have to increase my output size. If I know up-front I'll be printing the images, I'll adjust the output accordingly, but 300ppi is never my goal. I'm quite happy with 200ppi. Especially since most of my prints are on an 11x17 laser, which can't compete with the DPI output of a good inkjet printer. My .02 cents.
Edited to add - the 8000x6000 image size requested in the original post may be dictated by large format prints they display on their construction sites. If they have a print company that they regularly send their work to, the print company may have determined that resolution works best for their particular final print sizes and gave them that size to use as a standard when hiring their CG resource(s). I wouldn't necessarily take their request to mean it's the new industry standard.