Companies in the US are not required to provide a retirement plan. They do it for tax reasons, to be able to attract talent, and for various non-monetary reasons (e.g. company leadership believes in taking care of their people.) The company wants to provide the retirement plan as a 401(k) because it is attractive to potential employees for tax reasons.
These requirements you're looking at cover the minimums that the company must provide if they wish to provide a retirement savings plan, and to have that plan be a 401(k) plan.
At the same time, companies want to avoid people taking a position and working for a year, capturing a bunch of retirement benefits then jumping ship. So if you can begin matching on day 1, and there's no vesting period, a person could capture all that matching for a year, leave, withdraw the money, pay the penalty and taxes and still end up at a 40% profit +/- gains.
Establishing a maximum allowed for minimum starting age is just the IRS preventing companies from discriminating against younger employees. Establishing a maximum allowed for minimum time onboard before starting prevents companies from setting these too high as well.
From personal experience, I've never worked for a company with a minimum age for contributing, and never seen a plan that you couldn't start on the first check after the paperwork is processed. I've also never seen one with less than a one year vesting period.