If this is all-new development, wouldn't it be good for the emphasis to be on correctness and security, as part of the design and coding itself?

That's something that you use fuzzing as one way to detect a failure of, not as the means of achieving correctness and security.

I'm not picking on Ladybird here specifically. Chrome and Firefox provide constant streams of security vulnerabilities. But it would be nice if Ladybird didn't start with the same problems that might be attributed to huge legacy code bases.