I tried this. It breaks a surprisingly large number of sites (or perhaps not-so-surprisingly), and good luck trying to beat Google's captcha without a User-Agent header.
Good luck trying to beat ReCaptcha if you're doing anything that puts you outside of the normal web browser behavior as imagined by Google's Algorithm.
If User Agent Client Hints become the new normal, I'm sure anyone excessively denying requests will be flagged in the same way.
If User Agent Client Hints become the new normal, I'm sure anyone excessively denying requests will be flagged in the same way.