USENET READER wrote:

Name me a profession that isn't unionized that have
apprenticeships?

Two - though their apprenticeships aren't formal training.
- electronic technicians
- machinery mechanics.
(They instead depend upon years of exposure to different types
of malfunctioning "gear", including poorly-written software.)

No training classes can prepare these individuals for what they
may encounter. In fact, both are similar in a lot of ways to
your "medicine" example, where diagnostic skills can come only
from lengthy exposure/experience.