Any reasons why this is permitted?

We probably cannot say for certain: The essential answer is "because it is" or "because your reasons for thinking it shouldn't be differ with the thinking of those who designed the language" but we can't really speak to questions like "what were Microsoft thinking when they designed it such that...", unless perhaps someone is one of the privileged few to have sat in that design meeting and can be authoritative

SharpLab.io will, however, tell you what happens under the hood; it compiles then decompiles your code and shows you the result, so you can get an idea of what your code was transformed into by the compiler:

^{Note: swapped your numbers for other, non-default, ones so that identification of what was what can be maintained after the compiler changes the names}

A lot of the code you write is syntactic sugar for something else; here you can see your int k isn't buried within the switch, scoped to only "within the first case", but transformed into something else entirely.. It's thus legal C# because nothing prevents it not being, and you can rationalize that in a way that will help you remember it.. In a similar way, perhaps this looks like it shouldn't work:

    object o = "";
    
    if(o is string s){
       
    } 
    
    s = "";
    

s looks, to me, like it's created within the scope of the if, yet it's accessible outside the if.. You'll find a similar explanatory transformation if you run that through SharpLab..