Executing a frontend function on app start was requested here as well and is being considered.
Regarding variable access between applications, I am not certain its a good idea. Variables can contain anything and can be coupled pretty strongly with the logic of the corresponding application. Being able to access them externally might make it too easy to break things. Also it would be another dependency that might break, when the author of the underlying app decides to change how they use variables. Relations are pretty stable, but variables might be less so. Then again, frontend functions have similar issues and they can be accessed... It´s tricky.
Do you have a use case where external variable access is required or helpful?