In the key markets for these things - there is no presumption of parking. I imagine avoiding parking is the #1/#2 reason for most users would use this service (I'd include ride sharing here too). I specifically don't have a car in San Francisco because I have nowhere to park it.
When dockerless bikes were launched in other markets (e.g. Sydney, Melbourne) it really was a mess. Bikes thrown in rivers. Stacked up as hazards. In trees. On the top of stuff in general. And Melbourne is a much more bike-friendly city than many North American ones. But it was still a huge bomb. It's probably sensible for the SFMTA to at least consider the consequences and stage a rollout.
The SFMTA was actually being pretty co-operative. And for a government agency, they were moving pretty fast - i.e. getting stuff going in weeks/months. Instead, one of the companies launched early on St Patrick's Day. When the others felt they were losing first mover advantage, they did too.