The problem is that in general "code" can't do that because the code that's switching stack doesn't necessarily conceptually control the stack it's switching to

The problem is that in general "code" can't do that because the code that's switching stack doesn't necessarily conceptually control the stack it's switching to/from. One SS:SP might point to a userspace process, for instance, and the other SS:SP be for the kernel. Both stacks are "live" in that they still have data that will later be context switched back to. You might be able to come up with a convoluted workaround, but since "switch between stacks" was a design goal (and probably assumed by various OS designs they were hoping to get ports for), the race that meant you can't do it safely was definitely a design bug.