At the same time, I don't think your assessments are correct by using Rangnick and last season to somehow make the current Liverpool situation the same as those. For one, it's not just clout or hype that Klopp has. He's a really good manager, something Rangnick could not call himself. Not just a good manager, but an elite one. It's based on actual evidence.
Two, are you certain they have to get rid of Klopp? Meaning, that just because it's Klopp's fault he's not getting through to them anymore, and that they still are footballers capable of the level they have been at for years, does that still mean you get rid of Klopp? Or are they not also to blame for not being able to keep up their performances at the standard they were at for years? If they are no longer listening to Klopp and that Klopp's messaging is no longer getting through to them, don't you think they're replaceable?
I think he's only replaceable if he's gone completely rogue, meaning the way he gives messages or the messages he gives are both crap. However, if he's still doing the same as he did initially, but the players are no longer responding that still means newer players who have never heard his instructions or messaging can still be part of the rebuild.
To me, I still think that them getting rid of Klopp would be their biggest mistake. I don't think anyone they get will be better than him, and that squad is going to need to be rebuilt even if you get rid of him. On the other hand, players are replaceable.
The evidence to not trust him on a rebuild is 2 seasons with Mainz (relegation, and then failure to get them up), and one season in 7th place at Dortmund. I still think there is sufficient doubt in that conclusion to still think he can rebuild if given longer than 2 bad seasons. I at least would be willing to give him another season after this season to right the wrongs.