The minimum 1 week off policy is to force you to use your PTO. In addition to some of the other reasons already mentioned:
1. The company could be truly interested in your well being and wants you to take at least 1 week away from work per year for mental health reasons.
2. Depending on the structure of your company and the state laws, unused PTO time is a liability for a company--like an unpaid bill that could come due at any time. Consequently, the company must hold an accrual (cash in the balance sheet) for the liability. In a large company, this can tie up a lot of cash very quickly (ex 1000 employees, average salary of $1500/week, with 1 week PTO = $1.5 million). By requiring employees to take PTO and limiting carry over PTO, the company can minimize the amount of the accrual.
The company I currently work for is fairly generous with vacation time and used to have no limit on the amount that people could roll over. There were people that had been there for 25-30 years that barely took any time off who had over six months each of vacation and comp. time! Over a year of PTO in the bank!
The company sent a note out saying that the purpose of vacation time was to help people to maintain their work-life balances and that it was meant to be taken. Now, you can roll over two weeks on your anniversary date each year. If you rolled over two weeks last year, then you have to take everything you get this year. Anything you have in excess of the two weeks gets paid out at 50% of your salary. That's important, because it's meant to encourage people to use their vacation time for what it is intended for, and not as additional salary or a savings account.