Universal stuff carrier

Sometimes bags aren't big enough for a particular item you need to carry, not necessarily in terms of the volume of the bag, but in terms of one (or perhaps two) dimensions. What would be useful in such a circumstance would be a "bag" that despenses with the holding mechanism, relying purely on a strap to hold the object. No doubt such things have been used in the past and currently exist, but they do not seem to be sold in retail stores, despite their usefulness. Illustrations below.