At 7, isn't sports day really just a bunch of round robin 'games' designed to be fun rather than competitive?
I totally understand where you're coming from on this op. My dd is the same age and, although seemed fine (even excited) in the run up to sports day, I knew she'd have problems getting into school on the day itself. She's nd and she went into blind panic when we got there, complained of a 'bad tummy ache' (which we know is anxiety), refused to go into her classroom and just wouldn't move, stayed glued to the ground. But because I knew this would likely happen, I had worked out a plan b.
In the end, I said I'd speak to the school and let them know she was there, but that she could sit with me, no pressure, and watch and cheer on her classmates. Then, if she decided she wanted to join in with anything, she could do, but she was in control. Taking that pressure off really worked. Her relief was immense, her tummy ache began to improve and when she saw how the others were having fun, she even decided to join in a couple of activities and was so proud of herself. I was her safety net, which is exactly as it should be. The school were totally supportive of the approach, too, which really helped.
Could you take a similar approach? Often, when there's no pressure, children see that it's not as bad as they feared which does help them become more resilient.
If this isn't an option for you, then absolutely keep her home. 7 is still young, you can work on building her resilience in relation to performance anxiety more slowly over the coming years. But it does sound like something she may need some extra support with. Is she also a perfectionist?