In theory, you are absolutely correct.

But these regional "airlines" are little more than outsourced staffing agencies. If the model is not working, the work is either not performed and the agency is fired, or the customer (in this case the major airline) coughs up a larger fee.

Considering that the RJ pilot shortage is industry wide and it also seems obvious that the major airlines are onboard with keeping the RJs flying, the major airlines are ultimately paying for it one way or the other.