I honestly wish more toys came with their own bags! Not only does it make storing them easier, but it can help you tell them apart without opening the bags when they all look a little different.
One of my more recent toys, the realistic werewolf one didn’t come with any alternative storage option, and it’s so big that I don’t even think any of the storage bags I ordered will fit it 
At the moment, I think I’m leaning towards a multi-teir make-up storage box and labelling the bags/cords to store things a little neater