First off, a "cheap but okay bike" is not $150. I can't stand this (nor can most bike shop employees, who are really, really, REALLY fucking tired of people strolling in and having wildly unrealistic expectations for what a bicycle costs.)
Bicycles are not toys, and they should not be priced like one. They should be priced compared to the expense of a public transit pass ($60/month in my city for bus+subway), a scooter, or car expenses. How much is a typical monthly car payment?(Answer:$452) How much do you put into that car per month in gas? (Answer: about $250/month.) Insurance? (Answer: about $800/year) Etc.
Second: bike rental systems (these are not "bike shares", despite the popular bastardization of the term) are popular because:
- They can be used for spontaneous and/or one-way trips. For example, I'm going out with friends tonight, and they don't bike; I don't want to have to leave my bike at work. I rode a bike share bike into work instead of taking my for-transportation bike. Or maybe it's going to rain in the morning but the evening commute will be spectacularly nice. Or maybe the roads are clogged and the busses running behind; I can hop on a bike share bike.
- You don't have to store the bike. While many buildings are getting better at this, most don't have bike storage, and it's usually a bit of a pain. Same at many workplaces, though again, lots of places are getting better at this, in part because there's often a financial incentive from the health insurance company.
- You don't need to worry about maintenance and repairs.
- It's amortized, basically. Instead of having to spend $500 on a solid commuter bike, you can spend $X/month/year. And in some ways, it's easier to track for purposes of taxes on commuting expenses.
- They are heavily aimed at tourists, despite claims to the contrary. Looking at the deployment maps this is pretty obvious - they stations tend to be around touristy areas in many cities. Bicycles are the perfect speed for touring an area; slow enough to take it all in, but fast enough to cover a good amount of area.