If it can't fulfill this core function without the screw, it is valueless.
Of course, you can pawn the motorcycle for thousands of dollars, but for that, you would have to have a marketplace and buyers. You can also turn some parts into tools and probably repurpose the tyres into something useful.
But again, to do that, you would have to have the knowhow and the necessary tools and time for repurposing.
If you were in an isolated environment with no other people around and no additional tools, a motorcycle that doesn't function is as good as "valueless".
With that said, the motorcycle is clearly not value-less without the screw the same way it is not value-less without a rider.
The instant you dismount the motorcycle it is no longer physically capable of performing its function. Yet it of course still has value.
I don't think your comparison makes sense. A motorcycle is not broken without a rider; it is not being used to move from point A to point B, but it is capable of being used to move from point A to point B.
A broken motorcycle is not being used to move from point A to point B, however it is not capable of being used for that purpose. The broken motorcycle is clearly at a lower state than a functional motorcycle.
Perhaps a comparison that works would be (a broken motorcycle + a rider) is as worthless as (a working motorcycle + a broken/ignorant rider).
Neither can be used to move from point A to point B without the addition of their missing component.
If we assume I have the appropriate skills/training to successfully operate the motorcycle that is missing a rider can we not just as easily assume that I have the appropriate knowledge/materials to add the missing screw?
E: The point I'm trying to make is that it is the same scenario. We could argue over which assumption is more practical (how hard is to to find and install the screw vs ride a motorcycle) but that is a separate point.
The screw seems most important when it is the 'weak link'.
But the same is still true of all other components.