Comment by mjevans

Why would a specialized instruction be necessary? 'the stack' is stored in memory just like everything else.

Expensive is the (very slow for modern CPUs) operation of _writing_ that change in value out to memory at it's distant and slow speed compared to that which the CPU operates at, as well as the overhead of synchronizing that write to any other caches of those memory locations.

Maybe you're thinking of the trick of a band new page of memory mapped memory that is 'zeroed' but is in reality just a special 'all zeros' page in the virtual to physical memory lookup table? Those still need to be zeroed by real writes at some point, if they're ever used.