I am definitely not the first person to discover that pin loom squares can felt up wonderfully. All you need is yarn that is about 95 to 100% wool and some time on your hands and you can make any number of strong, usable felted bags.*
The bag examples below are the first two in a series of experimental bags that will hopefully encourage you to try an even better one of your own at home. The smaller felted bag on the left was made from a trove of wool squares that someone gifted to me, probably woven by an elderly relative a long time ago. Unfortunately, perhaps because I had not put in the time to weave them myself, I did not take proper care when I felted them, blithely throwing the bag into the washer and dryer with a load of jeans and towels. The result was that the bag is too tightly felted, overworked to the point that it looks weird and fuzzy.