Let's not think this is true for all cases. You have Xabi Alonso, Suarez, and Mashcerano, who've won a lot. You may have a point in case of how it would've impacted their own status among the fans (had they stayed), but as for silverware, you can see the facts for that.
As Skip was saying, the old saying was "The only way was down".
It wasn't like that for years because of the state LFC was in and the draw of the big Spanish clubs,
hence Alonso, Suarez, Mascherano, leaving. The perfect storm of club in crisis and Barca/Madrid.
Now though it's starting to look like Klopp has achieved his aim to make players view LFC as their end destination and not a stepping stone. Of course the club will need to build on that, in all areas.