Goals
Each change should have a goal. When we talk about processes, the goals of process changes vary depending on the type of project.
Startup. The goal of a startup is to prove or disprove the theory of the project idea's success. Accordingly, process changes/implementations should help achieve the end goal as fast as possible.
Product. Here it gets more interesting. When a project transitions into the product stage, the technical debt in its codebase quickly accumulates, which can consume a significant amount of resources if it exceeds acceptable limits. Therefore, process changes/implementations should help effectively fulfill business requirements while reducing technical debt and establishing a codebase that can serve for decades.
Outsourcing. Here it's quite simple. We build good processes to easily and seamlessly replace any participant in this process. This is the main goal of processes in outsourcing. However, we can also transfer the same goal to the product.
If you are modifying existing processes or implementing new ones, you must have a clear understanding of what results you want to achieve. People often try to solve a problem that is not the one they are actually facing.
Also, this goal needs to be communicated and proven to all participants in the process that is being changed. If you have not done this and there are team members who disagree with the new processes, you will not only fail to achieve your goal, but also lose the support of process participants, or even the participants themselves. It's important not just to show a ready-made plan for the new process, but to involve all its participants in creating this process - for example, to create a Software Development Life Cycle process, you must involve Software Developers in creating this process.