I don't live in NYC but we do have a bike share system in Minneapolis. I ride my own bike every day to work and felt much the same way as you did but I've since realized there are some significant advantages to using a bike share system.
The biggest for me is that I can get around town without having to lock up my own bike somewhere and risk getting it stolen or damaged.
Another is cost. An annual subscription to the bike share system is $60 or so but if you're savvy you can get them for $45 or less. My subscription this year cost me $20. That's far less than what an annual bike tuneup would cost IF you don't need any parts.
Then there is the space saving thing you alluded to. Though you may be fine with a bike taking up space on a wall in your apartment, not everyone is. Depending on what floor you live on, getting the bike into your apartment may not be at all convenient even if you have the space. And while yes, you could lock it up outside, again it is at greater risk of getting stolen or damaged.