Maybe it’s not about competing with cotton. Flax doesn’t deal well with what cotton needs, they’re not going to be competing for field space.
Linen softens with age, but it’s not knit cotton t-shirt soft. It could do well in jeans and duck workwear, more structured clothing. It might even find a place in bras.
Cotton could easily push out nylon fabric in casual applications, and less plastic is part of the goal right?
I really see space for both of them, especially if we’re trying to steer towards safely biodegradable fabric that can be composed instead of sent to a landfill to sit for the next 500 years.