They do, you should always use one of the other methods to close up the bag, then put it in the bin

Depends on the bread and the bin. My parents have a pottery one, it keeps proper bread perfectly fresh. Of course you do need to eat a bit at least every day/every other day, because the cut side will dry out eventually.

Maybe that's mostly the bread doing all the work though. I don't know how you can store toast for any practical amount of time without consuming more preservatives than bread, lol

If you leave bread fully enclosed in plastic, all the moisture from the crumb moves into the crust and makes it soggy. But it doesn't dry out.

If you leave it just open, it dries out.

That's why (real) bread is best stored in a paper bag or in an unglazed ceramic bread bin. Those two materials allow for a slow exchange of air, therefore keeping the crust crunchy and the crumb soft.