I graze pigs through wetland areas. After 4 years, the wetlands look fine
The pigs root around the edges of of swamps. The swamp rooting is a good thing - muck tends to anaerobic=acidic=on its way to peat. Aeration liberates nutrients to grow things
Marsh areas (grassy wetlands) don't attract a ton of eating interest from my pigs. My pigs don't root through it, though they make use of wallow spots.
Most scientific literature is dubious about pigs doing anything good, because they don't know how to raise pigs with low rooting behavior. I have finally been able to follow in Jeffries footsteps in grazing pigs without excessive rooting.
I have read scientific articles about grazing
cattle in wetlands that fingered lack of disturbance as the cause of excessive invasive
perennial species in wetlands. Wetlands in the wild do get disturbed.