I have checked duffle bags that zip but not those that tie. I wonder if the ties could cause any mechanical malfunction if a conveyor belt were in use for loading/unloading bags.
As far as the laundry facility on the ships, I have been carrying ziploc bags with pre-measured dry detergent for this. I am allergic to Tide and was concerned that it might be the only option on the ship. I just found a few weeks ago, some small sample size bottles of concentrated All liquid detergent. The bottle is enough for two loads of laundry. I will be packing those this time, along with my fabric softener sheets and a mesh laundry bag.
I also pack a couple of tote bags and a folding duffle bag to carry home more than I bring, including the dirty laundry