I hesitate to call it a problem because, by the way it's defined, subjective experience is innately personal.
I've gotten into this question with others, and when I began to propose thought problems (like, what if we could replicate sensory inputs? If you saw/heard/felt everything the same as someone else, would you have the same subjective conscious experience?), I'd get pushback: "that's not subjective experience, subjective experience is part of the MIND, you can't create it or observe it or measure it...".
When push comes to shove, people define consciousness or subjective experience as that aspect of experience that CANNOT be shown or demonstrated to others. It's baked into the definition. As soon as you venture into what can be shown or demonstrated, you're out of bounds.
So it's not a "problem", as such. It's a limitation of our ability to self-observe the operating state of our own minds. An interesting question, perhaps, but not a problem. Just a feature of the system.