It's because of anti-discrimination laws. In some US states it can be illegal to hire someone for a position without posting it publicly. The concern is that if you're not posting the job publicly, it can be because you want to prevent certain people from applying.

When you do post it publicly, the company can demonstrate that they allowed anyone to apply, show records that they considered multiple people for the job, and then decided on the internal candidate as the best fit. No room for a discrimination lawsuit.

Source: I'm a hiring manager at a multi-billion dollar company and have actually learned a thing or two from annual compliance training over the years.