The real problem of consciousness I can only speak for myself, but I don't think you've understood the view.
It has nothing whatsoever to do with whether scientists can study consciousness. Nothing. The point is a very simple one. You can't get out what you don't put in. You can't get a sized thing from combining sizeless things.
This argument is valid: 1. If umbrellas are up, it is raining. 2. Umbrellas are up. 3. Therefore it is raining. The conclusion contains nothing not already there in the premises. It extracts their implications, but it does not add anything. Whereas this is invalid: 1. if umbrellas are up, it is raining. 2. Umbrellas are up. 3. Therefore I am rich. That conclusion doesn't follow from those premises. Why? Because nothing it claims is in the premises.
Now unless you think that you can make a sized thing from sizeless things, and that you can validly extract a conclusion about wealth from premises that don't mention it in any form, then you accept that you can't get out what has in no way been put in.
Thus, applying that same principle to consciousness, you cannot get consciousness out unless it has been put in. Thus, if you think that a complex physical thing has consciousness, then you must - on pain of believing in magic - believe that some of its components had consciousness. Otherwise, whence came it?
Note: I am not challenging 'science'. Nothing in science challenges what I've just said. Nothing in science challenges the idea that you can't get out what you didn't put in. It is those who believe that you can get a wholly new kind of property from ingredients none of which possess it who are being unscientific.