No-one has mentioned the psychological aspect of terrorist attacks/mass casualty situations. One of the reasons so many soldiers who suffered complex polytrauma on operations in Afghanistan was that they received effective care from the point of wounding to the time they reached the Role 3 Hospital at Camp Bastion. This started with 'buddy care' by other soldiers, continued with the patrol medics, then the MERT. One of the key factors in ensuring that soldiers on the ground, including medics, were able to render effective immediate aid, was the training they underwent - as part of their normal work, but also - and significantly - in the run-up to deployment, and then consistent reinforcement. Soldiers are, of course, also trained to be able to overcome the effects of hyperarousal, or the fight, flight or freeze response. Even so, events outside their normal range of experience can still trigger instinctive responses. Another factor is that soldiers have been through a selection process. Interestingly, the Royal Marines, who undergo probably the greatest level of selection during recruitment and basic training, have significantly lower rates of mental health issues than the rest of the forces (although Special Forces MH data are not reported). HART paramedics undertake selection and specialist training for major incidents.
Emergency services staff attending major incidents such as terrorist attacks, who are usually able to manage stuff most people would find extremely difficult, can find it difficult to function, especially in the early stages. In other words, a major incident (one that is outside the individual's usual sphere of experience), may trigger a different reaction than a minor, or 'normal' one.
How does this play out when an incident occurs? Hyperarousal will see many people running away or freezing; sometimes it also appears as people appearing confused, or unable to concentrate properly. The response can also mean that people feel that time is slowed down (an example of this is people stating that events seemed to unfold in slow motion, or saying that emergency services took a long time to respond when in fact they were there quickly).
We can't generally tell how an untrained individual will react - until it happens. In the same way, recent research by KCH and in the US has found that trying to screen people to see if they are more likely to be susceptible to PTSD doesn't work. Imagining that you will be able to function normally in a major incident because you can function in other challenging circumstances is misguided and rather arrogant. Even the most mentally resilient people can turn into headless chickens in a critical incident.
For me, carrying kit like tourniquets (leaving aside the implications of misuse) and dressings might provide an individual with some reassurance, but I suspect that actually being able to use them effectively in the midst of a major incident is unlikely. If the person carrying them has some relevant experience, for example as a military medic, then the chances of effective use increase - but I suspect that most such people wouldn't bother. They'd use whatever was to hand in the immediate situation, and then hand over to the paramedics.
To head off the inevitable question, I'm a former forces medic who's also worked in civilian healthcare. I've worked in various conflict zones including NI, Bosnia, Iraq and 2 tours working in the hospital in Camp Bastion. I've completed Major Incident Medical Management and Support (MIMMS) training, and have acted as bronze commander during incidents such as aircraft crashes. I now teach mental health first aid & resilience to various sectors both civilian and military, including NHS ambulance staff, firefighters, police officers and SAR personnel. The organisation I work for was involved in providing support to emergency service personnel following the recent Manchester PBIED incident.