I suppose you could make a cheap laundry basket out of chicken wire, but there would have to be some way to protect from rust caused by damp clothes.
Unfortunately if you live in the US you're starting out at about $50 instead of $5. I think that's a little bit of a HCOL price point, though. I picked up a burlap shopping bag in India earlier this year for about the equivalent of five cents, that any store here would have charged a couple of bucks for.
Crap, if people just spotaneously started buying qualty, durable things, and companies actually made them, that would go an enormous way to help the global environmental collapse.
You have anyway lots of company. That should not be reassuring.
(I use "you", here, to denote all readers in the same boat, not any particular individual.)
Notice that the basket from the article has rounded edges, and rounded cutouts. The plastic appears to be thickish and should be very slightly flexible/rubbery (bending because the material is flexible, not merely because it is thin).
These products should (and definitely can) last decades.