Outsourcing can allow you to use skills that the company does not own internally. Convenience should, however, be assessed on the full service, including coordination, information exchange and error handling. The supplier's invoice does not describe the full cost.
In a hypothetical example, a support activity is outsourced. If requests arrive incomplete, the time saved can be absorbed by clarifications and corrections. Before changing your organization, you need to understand what information makes it possible to work well.
I propose to define observable outcomes and escalation modalities for problems. Response times and quality must also have a shared meaning: responding quickly without resolving the request can leave the customer in the same situation. Contractual conditions require a specific assessment.
The company should retain the ability to understand the service received and retrieve the information necessary to continue it. If all knowledge remains with only one supplier, replacing it can become difficult. A periodic review helps to verify cost, reliability and dependence. The relationship works when responsibilities and information flows are clear enough to allow control without rebuilding the work each time.