Most bicycles, though smaller than people, are much more inconveniently shaped and harder to manuever or get out of the way.

No more inconvenient than people with those backpacks with wheels.

A bicycle is dirty, greasy and has pointy bits. No more welcome in a building that other, um, dirty, greasy things.

Assuming your bicycle is properly maintained, it will not be dirty, greasy, or have pointy bits. Daily lubrication of the chain prevents it from becoming dirty, and a chainguard (or even better, a chaincase) prevents most things from touching it anyway. After that, no exposed part should be greasy or dirty.

I share my apartment with three bikes, and they are as clean as anything else in the house.

All scrupulously clean, except of course the tires which are exactly as clean as the gutter you have been riding in. Every part of a bike is a pointy bit, made abundantly clear when you go down and tangle with it. Transportation devices belong in the garage, not in the living room.