If the government wasn’t allowed to hire from private, it would be starved of talent. That would be a great scheme to hobble any agency you don’t like.
You can cut it more finely but I think you still run into the same issue. The best candidates to run an agency that regulates a particular industry are going to highly overlap with the best candidates to be leaders in that industry, because they have knowledge and experience over how that industry works.
Sort of like how many top law students choose between clerking at federal court and joining big law, or do one after the other. And people who become judges often did both. If you ban people who worked in private practice from being a clerk or judge, you would have a lower quality judiciary.
Ultimately, I think you end up with the B team trying to regulate the A team.