Its not about cheap bikes. The bikes break, are destroyed, left somewhere useless/dangerous, or are stolen/confiscated. The investment money that paid for them was leveraged (an investment/loan). The income from the surplus of nearly free bikes can't pay back the investors and retain their ridership. Meanwhile, people who live near a point of interest have to deal with a massive pile of dumped (possibly broken) bikes in front of where they work/live... and they pay a public price.
At $0.07/hour, with a bike cost of $80, the bike needs to be taken on 1,200 hour-long trips to recoup its investment. That's possible, but not in a city with 1 hire bike for every 16 people.
And this isn't even considering the bike repair, lost/vandalised/taken apart bikes, trucks needed to move the bikes when people's trips don't balance the bikes out (e.g. people riding public transport uphill and bikes downhill).
Even most publicly funded bike shares don't make a profit. They bring benefits to their city in reduced pollution and traffic, and increased health and enjoyment. None of which will show up on a start-up's balance sheet.