With bike sharing, you just leave the bike in a docking station and you don't need to worry about it ever again. The only problem with bike shares is if there isn't a docking station near where you want to go, which is at least a plannable inconvenience, as opposed to getting your bike stolen and needing to walk home 4 miles because there are no good bus routes near you.
And on a <$100 bike (or for that matter any bike under about $400) that'll be frequent. Department store "bike-shaped objects" are not known for their reliability
To be honest I think once you spend more than a few hundred dollars you're just paying for fancy suspension and fancy brand-name. I could of course be wrong, as I've never bought an expensive bike.
If I'm going some place that I can bring my bike inside, I ride my own bike. But for ~80% of trips in NY, CitiBike is more convenient (plus, if I meet up with friends, I'm not chained to my bike anymore, and can just use the subway like everyone else).
If you are discerning enough to buy a decent bike on (e.g.) craigslist for $50, and are confident that you can do any probable maintenance, the service probably is not for you.
If I was the program director though, I wouldn't be worried yet. We just got out of the coldest winter in recent years, and in a few months we can tell if no one is riding the bikes because the novelty wore off or because it was cold.