It's personal choice. I want to leave my properties in a better condition for future generations, so I don't use 'nasty' chemicals unless there's absolutely no alternative e.g. Killing invasive weeds (careful selective painting, never spraying), even minimising the use of PVC piping, etc.
So using synthetic materials in
land stabilising is a no-no because of the mutagens often used in their manufacture - downstream water quality et al.
As noted by S. Benji, Swales shouldn't be used on steep slopes (>15%) because of land slip issues, so some other alternatives may be more long lived e.g. Small terraces, a row of rocks or old
concrete, gabion baskets, logs pegged into place, etc.
Once plants get a foothold, nature takes over: nature hates a vacuum. (Aristotle must've been into
Permaculture too!)
So, I suggest allowing styrofoam to go to landfill in a few already polluted locations is better than spreading its toxins all over the place - including unsuspecting future generations.