As I understand it, the 89 year old lady would have used one of nos 1 to 4 lifts to the lower hall. It is most likely that the lifts were on rear door opening, thus pax would use the rear passageway steps to gain access onto the platform, which exits a little over a coach length along the Up platform. (This is quicker and more convenient than walking round the lifts into the lower hall, then using the wide staircase to the Liverpool end of the platform)
Those who remember the working of both Hamilton Square and James Street in the direction of the respective peaks prior to the Loop/Link scheme, will know that this exit onto the platform at Hamilton Square, and the two exits onto James St down platform, had pantograph gates which were manned by staff. These staff were instructed to close the pantograph gates as the train was running into the platform and not to open the gate until the train was part way out of the platform. The supervisors closely watched this.
Thus most pax joined quickly and safely and were not presented with doors closing in their face, unless they were very slow and did not join at the nearest door, or began to walk further down the platform, or used the wider staircase at the front of the platform. The underground station dwell time was 30 seconds, which was necessary to maintain 26 trains per hour in each direction. Off peak, no staff were rostered on the gates.
Perhaps a reccommendation may be made that Merseyrail devise a similar system to prevent access to the platform for a small amount of time? This would of course delay pax alighting, and leave the narrow platforms grossly overcrowded and dangerous, also where multiple entry/exits exist it could prove most difficult to enforce fully. So it would seem that the problem will continue until a solution is found.