To my way of thinking, the time to allow access to the platform in normal circumstances is after people have alighted and any internal cleaning has taken place, but still at least 10min before departure. That way passengers don't get in the way of other activities but still gives a reasonable time to board. If the turnaround is too short to allow this then either it needs to be longer or the internal cleaning should be reduced, for example by coming down with bags for litter before the train arrives. I believe this is what they now do at Euston, at least most of the time.
In the case of disruption when a quick turnaround is needed, then I suggest passengers should be allowed onto the platform before the train arrives, so they are ready to board (and some are on the right part of the platform for their reserved coaches) as soon as arriving passengers have alighted. There may be some conflict between them at the doors if departing passengers don't wait, but that's less bad than opening the barriers for a wave of departers to clash with a wave of arrivers, or lengthening the turnaround by not letting departers onto the platform until all the arrivers have all left (which could be some time for the slowest ones).
If any operational factors were considered when designing the current Kings Cross layout, then the basis must have been that platforms would be announced and accessible well before departure. As someone mentioned, the footbridge barrier can only work like that or be left open the whole time as it now is, otherwise queues will build up and render it useless for anyone else.