These are used extensively in erosion control management on construction or earthwork sites and I have both used and inherited them on sites where I've done veg mgmt.
In short:
They funciton for erosion control, not weed supression.
The jute/coir mesh products function poorly for mitigating raindrop impact (they don't cover enough) and then are LIVING HELL to plant through (difficult to cut every planting hole).
For large areas, seed followed by blown chopped
straw can work as well without the manufacturing costs of straw mats (both paid and hidden) and you can add depth where useful.
There are a range of applications where you actually have moving
water and need to keep soil in place until veg takes.
Washington DOT has largely shifted to
compost blankets (4 inches blown in) which provide very high erosion control value along with all the other benefits of compost and the ability to serve as a relatively weed free seed bed.
For low cost bought in material I like hog fuel on a conveyer truck for woody, or straw chopped and blown or hand placed and punched into soil with a knobby roller, using tackifier if facing liability.
Sorry for the language density -- happy to try to
answer specific questions.