Why would you assume those things aren't already on the motorcycle?
Oh, I do. But we are talking about 200 years here (23rd century). Tire rubber disintegrates, as do gaskets and other parts. If yoiu have ever owned a motorcycle, this question answers itself. Not to mention the gasoline issue. Why would it even be acceptable cargo on a starship?
These people travel faster than light and can make a ribeye out of pure energy. Pretty sure they could rebuild a carburetor.
As far as why it would be acceptable? Captain's prerogative.
It could be standard-issue for planet-side operations.
Picard also had a wheeled vehicle stored on the Enterprise-E.
Kor