Kernel security: beyond bug fixing

Is that an x86 thing?

On ARM, there are some shadow registers that backup the PC and the processor doesn't touch the stack itself - and rightly so! It's most efficient for the interrupt handler writer to decide what state needs to be saved and restored, particularly if the interrupt routine isn't going to do very much.

If a CPU did automatically push something on IRQ entry, you could still engineer an ABI that uses an 'empty ascending' stack where the stack pointer is maintained to point to the first unused word at the stack top.

I'm pretty sure you could run an ascending stack on ARM, probably other architectures too, but it would be for limited security benefits so moot.