IANA.. anything relevant here. I work in construction management (many years prior in IT, security, etc, hence me being here), and often at my desk on the jobsite the grinding, hammering, cutting, you name it gives piercing noise that makes it f'ing near impossible to concentrate. So I've been eager to use noise cancelling.. however there are issues.
The obvious one, pointed out, is possible cancellation of noise you really need to hear instead of ignore, like something collapsing, someone calling you, etc. (especially when walking the site instead of at the desk) In a construction environment, it'd be very hard to programmatically distinguish the good loud noise versus bad loud noise- scaffolding may be collapsing, or it may just be a steel worker cutting an extra toe angle off of a joist that was manufactured incorrectly and that falling to floor. It's probably kind of like if an active shooter scenario happened at a gun range- which gun shot is bad? You can perhaps tell by direction sound was aimed in that case, but standard folks listening will mostly just hear shots until they notice something amiss. (I pray I never experience that.) I suspect the best answer in industrial application would be "partial cancellation," a bit more noise let through than Bose currently lets through, kill plainly regular noises like compressors but let irregular noises like crashes or hammering through.
However, my sister is an audiologist and pointed out something else- there really hasn't been a study of noise cancellation in loud environments, and it's benefit to ear health. While the cancellation is creating opposing waves and all, there's no study on the actual sound pressure that gets to the ear drum and possible effects of that, even if it is in an inaudible range. I can say when sitting at my desk and I turn on cancellation with my Bose QC20i's, it does WONDERS for noises like compressors and such- but I can tell there's a pressure in my ear from the cancellation. So there's still a valid health concern to be investigated before they'd be OSHA approved for use- I'd rather not lose my hearing thinking the cancellation was a good noise reducer when it had negligible health effects. As such, right now OSHA doesn't really approve noise cancellation in any construction environment, just standard NRR rated blocking materials.