I can think of so many reasons it mystifies me that you seemingly can't think of one. A few:
1. They have no idea what subway is going to be down, and when (even forgetting about the "normal" service that isn't very normal nowadays), when they set the schedule.
2. Many people cannot make it by 7PM because of work, and many more can't eat and make it.
3. On balance, the inconvenience of walking a bit farther is slight compared to not being able to make it at all.
4. The transition from day to night is a part of the magic of shows in the park.
5. On hot days, that extra hour can be a godsend.
6. I don't recall "blinding floodlights." If the lights are too bright for you after dark, what do you do in a theatre which simulates nighttime even at a matinee? Perhaps you should consider sunglasses if you have a sensitivity to light that extreme. And even assuming these "way too bright" lights, that would be a complaint about the lighting design, not the time the show starts.