And how do you replace this text without losing important, non-origin context? What you probably need is an entire re-write. But a re-write, or even a bad text replacement, can make it look like the applicant is better or worse at grammar or writing in general.

This is not as easy a task as a simple text replacement.

The important content is their work history, projects, technical skills, etc. If the rewriting is awkward, it's affecting all candidates uniformly.

A genuine bad rewrite would tend to affect all candidates uniformly (except those who have pre-anonymized their applications, thus gaming the process), but a find-replace is more problematic.

If that's an issue, the companies could just tell applicants to pre anonymize their resumes to eliminate any potential gaming.

I think it's worthwhile A/B testing your idea.