Wow! I found that there's a breakwaters project in construction in Tottenville, in Staten Island. It was designed by SCAPE, Kate Orff's office.
Aha! And they established a Living Breakwaters Curriculum to teach students about breakwaters!
But I finally found a Pros and Cons list for breakwaters. It lists the major 'con' for fixed breakwaters as cost. Which seems a little silly to me.
This wiki page on Coastal breakwaters dives deeper into the weeds of hydrophysics which I really appreciated. However, I think this is opening up more questions for me and it feels a little discouraging.