If you took out a loan to pay tuition, the loans don't disappear. Isn't this basically the same thing? The employer is loaning you the money to cover training with loan forgiveness for time worked.

No, because the employer isn't loaning you money. In fact it would make much more sense if the employer gave the employee money as a lump sum in exchange for some agreement, much like a relocation or signing bonus. Instead this is the employer pretending its training is worth real money on the real market. In the Reuters article, an esthecian was charged nearly 2k for leaving a shitty job because of "training", despite already independently having the license necessary to do the job and no one reasonably paying that beauty parlor 2k to be educated.

Additionally, certain education-related loans do in fact disappear! Loan forgiveness is a real thing.

Schools are highly regulated. Loans are highly regulated. Education from colleges is accredited and held accountable to third party institutions. Employers training you then charging you isn't regulated at all. It's ripe for abuse and clearly abuse is taking place to the woman in the article.