There are folks out there breeding foundation lines. We used to have one here. To be registered as a foundation Morgan they have culled out the Saddlebred lines that were added since the 30’s I think.I don't consider what you're seeing now a Morgan. Your physical description of them is what a Morgan is.
The only way to protect the breeds as we know them is to breed them ourselves. Well, not me since I don't have horses anymore.
I never found the physical appearance of Saddlebreds very appealing.