My answer is that I do not believe in woven membranes for paths.
I think that the more tradional method of a hardcore base followed by sand and finally washed gravel
This gives a proper passage of water through the soil.
If the construction is done correctly there should be no signs of weeds.
Paths are often built badly using membranes.
The result looks a mess after weeds start to appear.
Woven membranes do have there place in borders to help reduce weeds.
This does not mean they should be used everywhere.