> Wouldn't a company have to post every single position because of labor laws, etc
No, labor laws in most of the US do not require posting any positions, much less every individual position. (Civil service may require posting civil service positions individually, or at least explicitly identifying the individual positions being hired under a combined posting, and labor agreements may specify requirements for how and where union-represented positions are posted.
> They can't just have one generic position to cover many
Yes, they can.
> That would open the doors for bad hiring practices and just picking anyone you want (without proper due diligence) rather then the best candidate possible.
Bad hiring practices are not generally illegal; those that are (racial discrimination, for instance) are prohibited directly rather than by prohibiting things that might open the door for them.