You cannot "strip off and rewrite" headers without destroying the email message's DKIM signature -- which is the primary assurance of authenticity of incoming email!

Also, you are ensuring that emails from your domain can never reach anyone who has a "forwarding" email address (which is anyone managing any significant number of domains). These people use Cloudflare, etc. to manage the MX for these domains, and forwarding incoming email to their central email address (which remains hidden).

You can't get away from email forwarding; its sort of baked into the underlying assumptions of SMTP, which you are unlikely to single-handedly defeat and replace with something better.

In the mean time, email from your domain will appear "broken" to a vast multitude of the world's email-receiving population.

Your domain, not theirs.