Point of sale in a records store, less important. Point of sale in a pharmacy, could be problematic. Web shop customer call center, less important. Emergency services call center, could be problematic.
Outside of regulated industries it's the context in which software is used which determines how critical it is. (As you say.)
So what you seem to be suggesting (effectively) is that use of software be regulated to a greater/lesser extent for all industries... and that just seems completely unworkable.
So if you develop your compression library it can't be used by anyone running critical infra unless you stamp it "critical certified", which in turn will make you liable for some quality issues with your software.
That's very realistic and already happens by requiring certain standards from the resulting product. For example, there are security standards and auditing requirements for medical systems, payment systems, cars, planes, etc.