> Why not both?
This is not a good idea. There is a conflict of interest here. The fundamental goal of government is regulation, the fundamental goal of a business is profit.
Both the morals of government and corporations are therefore very different. I call them Guardian and Commercial Syndromes respectively. When you combine these two syndromes you create monstrous hybrids.
Allow me to elucidate:
An entity in the Guardian syndrome values honor and uses forceful tactics to maintain order and regulation.
An entity in the Commercial syndrome values money and tries to use whatever means possible to gain profits through trade agreements.
You don't want a commercial entity to have the power to enforce things and you don't want a government entity to desire profit. Both hybrids lead to bad things and it's the root of corruption in the world today.
You know how the old medieval English Nave formed? So many pirates lurked off the coasts of medieval England that London merchants went to the expense of financing a fleet of fighting ships and gave it to the Crown.
Why give it to the Crown? Because you don't want some commercial entity running the Navy using methodologies that circumvent trade agreements and violently funnel trade and profit to a singular commercial entity. You need an entity outside of the commercial sphere; An entity in the Guardian Syndrome. If a commercial entity controlled the Navy you get something similar to the Mafia or Yakuza; Basically organized crime.
Only the government should enforce the laws of AI because there is in theory no conflict of interest. But practically speaking the US government is pretty heavily hybridized already (See military industrial complex). Still it's the best option.