If I may add a couple of points to what LFH has posted and what is in the linked documents. I flew the Hawk T1 for over 40 years, instructed on it for 30 years and flew quite a few non-aircrew in the rear seat. I also authorised many others for the same activities.
My first point is with respect to PEFATOs. We flew these fairly regularly adhering to very specific minimum airspeeds and energy states (combinations of airspeed and height). Often, we recognised that we had insufficient energy such that we flew a go-around (and for real would have ejected). There was never any pressure to continue and if it was an instructional sortie or checkride then the required standard related to correct decision making and not actually touching down on the runway. Overall, if the SOPs were followed then I did not consider these to be particularly high risk manoeuvres and stall prevention was achieved by strictly adhering to minimum speeds and maximum bank angles. The speeds flown and the energy states during the accident manoeuvre were significantly lower than what I had ever known to be taught or promulgated. In addition, 'low key' for a low energy pattern such as this needed to be an energy state and not a geographical position with respect to the touchdown point as was usually considered for a full forced landing pattern. For continued safe operation of the RAFAT aircraft prior to any of the suggested modifications being incorporated, have the SOPs been reinforced and/or amended to take into consideration energy states and minimum speeds when engine out, for practise or for real? I am sure that they have but I have not seen any mention of this reported.
With respect to using flight simulators for PEFATO training, the pilot needs to maintain a visual sightline to the runway at all times during the pattern, and the visual systems of many simulators do not allow this (vision being limited to forward of the '3-9 line'). Therefore, if on-aircraft training were not permitted any simulator used would have to have an adequate visual system to allow the pilot to use the same visual cues as for real.
There was a significant ambiguity in the Aircrew Manual of which there has been little mention. It stated that the minimum airspeed once the gear and flaps were down was, at the accident weight, 155 KIAS (170 KIAS being the nominal airspeed). However, what it should have said was that this was the minimum speed at which to commence the flare to touchdown (in order not to stall) but some interpreted this as the minimum airspeed in the finals turn also. I consider that this ambiguous wording was one of the greatest potential risks for stalling during forced landing patterns and I always reinforced this clarification very strongly in all training that I delivered.
I do not believe that the decision as to whether non-aircrew can fly rear seat in aircraft such as the Hawk T1 is necessarily just a simple yes/no. It may be an overall no (with a potential for reducing morale and motivation for groups such as 'The Circus') but there is also the consideration that it could be a 'yes' but only for lower risk activities such as transit flights. I have certainly operated such that we would not fly any forced landing patterns, or one engine inoperative patterns if multi-engined, with passengers on board. Similarly, in later years low flying, and low level aerobatics/display flying (under civilian regulation), were not permitted with passengers on board.
This was such a tragic accident and however much Jon may have understood and accepted the risks it is his family and friends who will continue to be affected. This is the one aspect that must never be forgotten when considering the future.