Unfortunately this idea would involve a massive amount of developer work, especially testing every single story dungeon. However, Castrum and Prae should absolutely be given a Trust system as these are the two most problematic instances, requiring both their own roulette and forced cutscenes simply to function.

What could also help a lot without taxing Dev resources is to simply bridge the 60-70 gap with a few Squadron dungeons. Even if it was only Sirensong, Shisui and Doma. That would cover 20-71 via Squadron, allowing the Trust system to take over from there.