static mutable member variables in C++?

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why or for what reason is it not possible to declare a class member variable in C++ as static mutable? Something like

static mutable int t; //This won't compile

For me, there is no reason to ban such declarations. E.g. for reasons like maintaining a global class-wide statistics, it may be convenient to have static variable that can be altered by (logically) const methods. So either this is sort of a misdesign in C++ and unnecessarily complicated, or there is a practical or theoretical reason which I cannot see.

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