If it is an individual's blog, direct link. If it is a news site that has a paywall, cookie popups, or other annoyances, I share the archive.org or .pH link.

There are a few other reasons I know of:

1. Archive.org links tend to pass through the paywall on sites that have them, so it provides opportunity to view content without that hiccup.
2. Digital sustainability is really hard. Many links have a short lifespan, or articles are "evergreen" and end up changing from when the post was made. This creates a snapshot to prevent both these issues.
3. Prevents the "hug of death", when an unsuspecting site goes from 1k visitors a day to 500k. Not all sites are resilient to that kind of traffic shaping.

Agree that it does bypass the good sites, but some have concerns over these points.

That said, you're placing your faith in your archive site to stay up and continue to function.