How can I stop CAPTCHA from repeatedly appearing in Safari?

I like to always use Private mode when searching Safari and for the past several years (at least) I usually get the “Our systems have detected unusual traffic from your computer network. This page checks to see if it's really you sending the requests, and not a robot. Why did this happen?” And then sometimes I have to “do the pictures test” which doesn’t actually work sometimes.

I don’t want to stop using “Private Mode”, I don’t want to stop using private relay, I don’t want to sign into a Google account, I don’t want to use DuckDuckGo or Chrome or another search engine..so what can I do? Are there any solutions? Why can’t Apple fix this? I live in a rural area so is that part of problem?

[Re-Titled by Moderator]