The problem as I see it is density & transportation tying our neighborhoods together. The areas/cities that this works in are HIGHLY condensed where people/bikers are able to move around easily from one neighborhood to another. So you could say, rent a bike in Avondale to take over to San Marco or up to Springfield, then be able to drop off the bike there & take public transportation back home. Jax doesn't have that type of setup at all. Even the "core" here is spread out. Meaning you simply cannot easily get to each of our urban areas without a car. You could probably string something together, but it would be a PITA & defeat the purpose.
So the sad reality is, until we get better connectivity & better public trans, this isn't going to be an option for us. People will just opt to stay in their cars unless you're able to take them out of the equation completely.