There are full auto m-14’s available.
You can bid on this one in an upcoming auction if your pockets are deep enough
https://www.youtube.com/watch?v=U3iFZSKXRcU
Shooting same gun
https://www.youtube.com/watch?v=VAABMvmaGWQ
Interesting, and it makes sense. These guns were never inspected and accepted by the government which is how they made their way to the market.
I now recall seeing a picture of one of these with the flash suppressor which were copied from the British .303 Jungle Carbine. I’ve never seen a real one.