Hi ChaseC99,
We see you're having an issue with repeated CAPTCHA prompts in Safari on your iPhone.
While you've taken some great isolating steps so far, CAPTCHA prompts are triggered by the site or sites you're visiting. For example if you're using Google to search and it's constantly prompting you, Google sees either your IP address or your device's specific Wi-Fi address as something to verify that searches aren't "machine driven".
We'd recommend looking over the steps in the following article to confirm they've been taken, and if the issue persists past that, reach out to the developer of the site you're visiting for further assistance on why your searches are bringing up the CAPTCHA request.
Cheers!