> Apart from the fact that not everyone uses Visual Studio, "connected services" appears to be something by which you can connect to existing cloud-based services.
Yes. That's the point.
> How does that solve the problem of a mess of interconnected services (...)
I don't think you got the point.
The whole point is that you only need to connect your local deployment to services that are up and running. There is absolutely no need to launch a set of ad-hoc self-contained services to run a service locally and work on it. That is the whole point.