Coming back to this discussion a few days later as I've just started an online course on Kubernetes from the Linux Foundation and I came across this section in the introduction materials that seemed very relevant here. Quoting from it:

  Training/Certification Firewall

  The Linux Foundation has two separate training divisions:
  Course Delivery and Certification. These two divisions are
  separated by a firewall. 

  The curriculum development and maintenance division of the
  Linux Foundation Training department has no direct role in
  developing, administering, or grading certification exams. 

  Enforcing this self-imposed firewall ensures that
  independent organizations and companies can develop third
  party training material, geared towards helping test
  takers pass their certification exams. 

  Furthermore, it ensures that there are no secret "tips"
  (or secrets in general) that one needs to be familiar with
  in order to succeed. 

  It also permits the Linux Foundation to develop a very
  robust set of courses that do far more than teach the
  test, but rather equip attendees with a broad knowledge
  of the many areas they may be required to master to have a
  successful career in open source system administration.

Running with this idea a bit, suppose schools were organized this way, with a similar "teaching/testing firewall" across everything they do. This doesn't get us all the way to solving problems around "teaching to the test" but it does put in place separate entities with the explicit mandate of making tests less 'hackable'.