Correct, but you actually can sell them as long as they are not manufactured with the intent to sell. So you can't make a lower, take it to the range for a day and immediately sell it, but if you have one that is several years old it's probably fine to sell it or give it as a gift.

And my understanding is that it is generally considered a good idea to add a serial number, even if it's not legally required. It can make interactions with law enforcement easier if they're not aware of all these details.