Your software just isn’t mission critical

Great point. I think part of the problem is that lots of people and organizations are convinced that people won’t work hard or well if they don’t feel like what they are doing is completely and utterly irreplaceable. By invoking the kind of language you’re talking about you escalate every possible issue to something that needs YOUR BEST EFFORT EVER RIGHT NOW. That might get you short-term benefits in additional productivity but you’ll burn out even the most motivated people if you’re essentially hanging a giant weight over someone’s head all the time.