I found a bug that seems to impact LabVIEW 2019 and 2020 on Big Sur (macOS 11) -- there's no problem on Mojave (macOS 10.4), from what I can tell.
Please see the attached VI for a demo of the bug.
Note: to even get LabVIEW running on Big Sur, you'll need to apply the solution/fix in this thread: macOS Big Sur: Labview crashes on launch
The issue is that setting FP.Closeable = False while FP.State == Closed gets the Close Window button stuck in the disabled state.
This affects the VI even when it's idle
The fix is to set set FP.Closeable = True while FP.State == Closed.