My two cents
To be honest, if you ask yourself that question, most likely, you don't need a service blueprint. If you don't see the tool's value, don't use the tool. There is no need to use the sexy tools of Service Design that everyone uses if you don't see the value it can bring to you.
For me the biggest reasons why I use service blueprints are:
Service Blueprints are good as an ideation tool: they help me quickly imagine new service ideas in a structured way
Service Blueprints are a good prototyping tool: they let me present and test an idea internally and see if the idea is feasible.
These are my favourite reasons to use a service blueprint. Outside of that, there is the obvious reason which is that it's a good mapping tool that helps people create a common understanding of how a service works or where a service needs improvements.
Service Blueprint resources
You can find all the Service Blueprint resources I've created here. This includes courses, templates and a library of external links and resources.