Why the compilation error for local variables?
The effectively final rule only applies to local variables and not global variables and for that reason, there is no compilation error for the first scenario as you're mutating a global variable.
If it helps capturing an instance variable can be seen as capturing the final local variable this so there is no compilation error.
Why is there such a restriction?
The book Java-8 in Action has a valid explanation for this restriction, it goes as follows:
You may be asking yourself why local variables have these
restrictions. First, there’s a key difference in how instance and
local variables are implemented behind the scenes. Instance variables
are stored on the heap, whereas local variables live on the stack. If
a lambda could access the local variable directly and the lambda were
used in a thread, then the thread using the lambda could try to access
the variable after the thread that allocated the variable had
deallocated it. Hence, Java implements access to a free local variable
as access to a copy of it rather than access to the original variable.
This makes no difference if the local variable is assigned to only
once hence the restriction. Second, this restriction also discourages
typical imperative programming patterns that mutate an outer variable.
