"important" is such a loaded word that I think it becomes useless in this kind of discussion.
I used to sail as a teenager, and boats with motors generally make way for those under sail.
Special privileges are not always a bad idea. Cyclists yielding at stop signs is one difference that makes sense to me, for instance. So do rules that exempt bicycles and tractors from enforcement of minimum speeds and "impeding traffic" violations.
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The bicycle, the bicycle surely, should always be the vehicle of novelists and poets. Christopher Morley