save any money by employing their own transcriptionists. They would have to have a department to hire, train, supervise, and manage the transcriptionists. They would need to have their own QA department. If the transcriptionists were employees, they would have to provide benefits (not an insignificant expense) and incur other expenses associated with employees.
Handing transcription over to an outside company frees up administrative personnel, equipment, and expenses that the hospital can use in other areas that are higher on their list of priorities.
The cost of using an MTSO is not the entire financial impact on the hospital. There are facilities and administrative cost reductions associated with outsourcing that makes it an appropriate business decision.
If you feel strongly enough about your proposal, write it up and present it to a hospital. You'll have to include all the expenses associated with your proposal and measure them against the costs of using an MTSO to prove your point, though.