No, gold ownership was made illegal in the 30s for a very specific reason: the dollar was pegged to gold, and there was a run on US gold reserves by foreign noteholders demanding redemption.
Also more ‘dollars’ had to be created. The only way at the time to do that at that time, was to have the gold to back it. That is why people had to surrender their gold and got ‘certificates’. The only exception was for gold in the form of coin.
Now that the dollar is not pegged to gold, it floats freely against it, so I don’t know why private gold ownership would be outlawed again.
No need to outlaw it. Coin dealers or sellers of gold coin like to drum up this fear since in the 30’s, the only way you would not have your gold confiscated was if it was in the form of coin.