Signing Rivers would open up the possibility of trading Rozier to someone like Phoenix and not adversely affect guard depth.
I would probably consider this if there was a return to be had. But then again, I was driving the "trade Terry + Sacto + Celtics pick for Wendell Carter or Jaren Jackson Jr" bus before the draft, so this isn't revolutionary for me. Plus Rivers is ok, and might have a higher floor than Terry too, though obviously Terry has higher upside and if Kyrie is hurt, Rozier is way more valuable.
The voice in the back of my head that says it's a bad idea, beyond the possibility of a Kyrie injury, notes how well Rozier seems to play with Hayward and Brown when they're all on the 2nd unit together. Hayward sets people up so Rozier doesn't have to, and Rozier is free to play off ball and look for his shot or to keep the ball moving to the open man. He's played well with Hayward, but if Hayward will be moving back with the starters, I fear Rozier will tail off.