I think you are excluding other scenarios:
A business may not be able to pay minimum wage and training costs. The solution there is more qualified people (but they take better paying jobs), lower wage (legally impossible), pass increases on to consumers (higher wages paired with higher costs). Wage increases can't magically be absorbed, especially in service industries with plenty of substitutes. Customers will just disappear.
The best example I can think of is restaurants closing in NYC because the increased wage costs due to increased minimum wage requirements made certain business models unsustainable: http://thefederalist.com/2018/07/16/15-minimum-wage-hike-wre...