Stopping blood loss is so critical that even the military changed from the ABC's of first aid (airway, breathing, circulation) to MARCH (Major hemmorage, airway, respiration, circulation, hypothermia). No one survives massive blood loss.

I vaguely remember the aid training shifting in the late oughts from a kinda checklist/hierarchy of things to do before applying a tourniquet into something close to "when in doubt if they might need a tourniquet, put a tourniquet on it."

Aside from the reasons you gave, I think it probably came down to the fact that there was an expectation that you would be getting treated by an expert in a hospital or purpose-fitted vehicle within an hour (whenever life/limb/eyesight was in jeopardy)

I have a lot of mixed feelings about my country and my service, but am still very impressed/proud of the extreme lengths the medical corps and supporting units went through to make MEDEVACs and treatment such a priority.

OK, prior caveat: This will be a long post and will not directly cite publications for every claim

So first off, I'll say that my advice on the topic is informed by (but not infringing on any intellectual property) my time working as a 911 dispatcher using data-informed protocols for prehospital treatment by laypeople (created by a Salt Lake City-based organization that is generally recognized as the standard for these protocols, and which sells them to most public-safety emergency answering centers.) [Bohm and Kurland, 2018] While this raises doubts about its accuracy, it establishes its uniquity] I understand that instructions for tourniquet use by non-healthcare personnel is changing as newer data shows that, as you said, improperly applied tourniquets are not as harmful as once believed and that laypeople can apply tourniquets effectively and quickly with proper instruction. [Scott, et. al. 2020] I believe that the previously mentioned company may have altered their product to reflect this, but I've been out of that gig for a few years now.

That said, the reason why (at the time) laypeople were generally not advised to apply tourniquets in the absence of unambiguously lethal, uncontrollable hemorrhage was not that a poorly applied tourniquet could worsen the outcome for a person with an otherwise lethal hemorrhage. Instead, it was to discourage the use of tourniquets when not necessary, as it was believed that a layperson may not be able to make this distinction and thus use them excessively. The vast majority of prehospital appendicular bleeds probably do not require tourniquet use (anecdotal, but it was probably close to 1 in 100 during my time answering phones). This is probably due to the low threshold some people have for requesting emergency medical transport. For a layperson who may have trouble telling the difference, attempting to control bleeding by direct pressure first is often a good idea in the absence of unquestionably uncontrollable, arterial (or massive venous/tissue capillary bed) hemorrhage.

TLDR: Until recently, tourniquet use by untrained laypeople was generally discouraged, but things have changed within the past few years.