It really shouldn't be weekly time-gated or anything of the like. It should be based on how dedicated a player is on getting the piece e.g. if they focused on farming high level mythics non-stop they would be able to get it within the week. Basically effort put into getting the piece should be worth more than waiting and the weekly mythic chest should be there to support them towards their goal and to be a boon to those who don't want to farm mythics endlessly. So I guess playing timeframe one week or less for people seriously going for a piece and one-two weeks for random and two-three weeks for specific for people playing casually and banking on the chest boosts more.