Totally agree. Lidded container does the job just as well in most cases.
We're using beeswrap stuff a lot more now for covering bowls - waxy cloth that's moulds to fit round stuff. Splendid. Pricey, but lasts a very long time once you have it.
Also using cotton cloth squares - like a massive hanky size - to wrap dryish stuff like filled rolls. Make the clothes from old sheets that have got worn out. Tie up the corners or stuff into a bag to hold it closed, or a bit of string or Velcro or elastic band.
And cloth bags for storing bread, cake etc, again, made up from old clothes or bedding.
I made some little bags with slightly elasticed tops for the kids to take fruit for school. Protects the fruit from knocks, washable, and has their initials stitched in so no labelling problems any more.
I actually think the fruit bags for school could really take off because they are so convenient to use. Can't be arsed to try and sell them, but if anyone here is a maker, they're a great thing and no one else is doing them as far as I know. We have three in circulation per kid, including a long one for bananas.