Impossible you say? Hardly. I got the idea when I was looking at a concrete parking stop. You know, those little gray strips that keep you from driving a car too far forward in a parking space. Well, what if instead of those, we installed bike racks and kept the striping that's wide enough for a car?
These would serve the same purpose for cars: keeping them from driving too far forward. It would also serve as a place to park a bike. First come-first served. Mode-neutral parking. I like it because it's not a zero-sum game. You're not building bike parking at the expense of cars or pedestrians, you're expanding the concept of a vehicle parking space to include bikes. This makes it politically realistic in a region where most voters still drive most of the time. Share the road, share the parking.
By the way, you'd be able to fit about 3 bikes per space using this design and it would only cost a few hundred dollars per space. Considering the fortune we spend on other modes of transportation, it seems like a very reasonable public investment for retrofits, and a reasonable thing to require in zoning codes for new construction.