Having the same issue …
Same as what? Your post makes no references.
… with Photo Booth saving corrupted videos.
It works fine on my Mac?!?
How do you determine that videos are corrupted?
Have you tried recording a movie in QuickTime Player? Should be roughly the same, except the filters.
I don't understand why AAPL has not yet fixed this issue?
Maybe the issue is not with Apple’s software? Then there is nothing to fix.
For macOS troubleshooting, try these:
Let us know the results of these tests.
Is there a reliable and free way of recovering the corrupted videos I've already recorded?
If the video is indeed corrupted, then that may be the only data available, and then there is nothing to recover.
If you have a backup of them before the corruption, then you can revert to a previous version.