Yes they do, but they hide it. On the plans page,[0] if you click "see all plans", a true monthly subscription option appears. But the prices are unreasonably large to force you into the "annual, billed monthly" trick. For example, the full creative suite (Creative Cloud Pro) is $35 "a month" with the annual contract, or... $105 on a monthly contract!
[0]: https://www.adobe.com/creativecloud/plans.html