What are these grommets (= snap holes / snap-rings?) on tool cases for

Those are grommets, not snap-rings or snap holes. Grommets provide a permanent ring providing an anti-tear resistance.

They are used to hang the tool roll from nails/hooks on a wall, for easy access to the tools in the roll. This would need fewer hooks than hanging each tool separately.

This is pretty rare in my experience, most workshops would hang tools on pegboard, or lay out the tool set in a drawer, or store the whole lot in a toolbox. I have one roll of ring spanners like this that lives rolled up in my car.