I've been to places here and Utah where pottery shards are abundant. One in particular in New Mexico called Ojo Caliente where there were shards too many to count. Some of the kids at the Pueblos will sell pieces. Some ask 50 cents.
They are protected so I leave them be.
There are theories why the pots are broken up (intentional) . Maybe they just got cracked and tossed. Just because we value them doesn't mean the potter did.
Cool find.