Hiring is an important skill for every successful company and the more you use these centralized services, the more you will be dependent on them.
At some point they will realize this and start calling the shots and because you now have none of the required hiring knowledge, you are stuck.
Where a third-party can help is in doing the things that are common across employers - a layer of screening that covers many of the soft skills and hard skills specific to that job type, but not specific to the company. Most employers don't do that very well. A third-party benefits from its expertise and focus - intellectual economies of scale, if you will. It can also make the experience much better for candidates. The status quo experience for job-seekers is terrible.
Their hiring process was delegated to non-recruiting function hiring managers, and had no structure to it whatsoever. I met with two different people I'd have been working with, and neither had any idea how to structure an interview, or ask questions that provided them the insight needed to determine if I was capable of doing the job. There were all sorts of questions about what I've done in the past, but nothing about what I intended to do, or how I'd apply what I know to solve the specific problems the job was created to solve.