Taysom Hill was the third string QB in 2020 when Brees got hurt against the 49ers. Winston came in to replace Brees, then Winston backed up Hill who was named the starter for the four games Brees missed.
A huge amount of this comes down to preparation and style. Haener is very similar to Carr in style so an offense built to Carr's strengths can best transition to Haener in an mid-game emergency.
Rattler is capable of being much more mobile than Carr and Haener and things like designed QB runs suddenly enter the playbook.