There are just too many places for people to garden. Everywhere I look there are vast open spaces that just sit there, many of them ugly and a mess and they've been this way for years. Likely the land owners don't want liability in case someone chops a finger off or some such thing but the likeliness of something like that happening is so unfathomably small that it shouldn't even be a factor.
I'm not talking huge crop farming either, just plot gardening with hand tools and a little elbow grease. Not only would it cut back on the amount of mowing and ground keeping, since the garden would be tended, but it would look better too.
Looking around at people at the mall or driving along in their cars I doubt that there would be enough people who wold care to take them up on the offer even if it was there. People in this city just don't have the roots that make gardening worth it. The average time spent in one house is less than a year on average. Some of the more permanent residents have their own gardens already or aren't as interested.
In some of the surrounding cities it would be more likely to have a centralized gardening area since more of the residents are less transitory and have roots and ties to their neighbors. For most community gardens in nearby cities there seems to be a group already who just want a little more space and a place to get together. Gardens tend to be from twenty to fifty people and tended by a fairly small reigon of people but there still aren't very many compared to the population.
The hot months in Texas don't make it any easier. Daily watering is a must for any garden to survive and if it's too far to go every day then it's hopeless unless you have someone watering for you.
In short there probably won't be a centralized garden any time soon unless people start setting down their roots and making a home and learn to rely on eachother for getting things done. In today's society that alone seems nearly impossible.
It could happen.