I suspect a professional sports team would not be particularly interested in demobilizing their operations and packing all of their equipment away every night, and then setting it up and cleaning out the food wrappers, dog shit and garbage left by community users every morning. (Even if there's not a lot of obvious debris, you need to check and clear the entire field before having professional athletes running and tackling at full speed on it.)
You were talking about sites that could hold "outdoor fitness classes, farmer's markets, watch parties" as a source of public benefit; you don't need a CFL sized-and-shaped field for those. The Beltline and Bridgeland farmer's markets both use around 2000 sq m. I can't imagine outdoor fitness classes or viewing parties (of what?) taking up more space. Here's contiguous open public grassed areas of around 8000 sq m in red (same size as CFL), 4000 sq m in orange and 2000 sq m in yellow. (interestingly neither farmer's market site is on my map because I left out areas with a lot of paving).
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