Dumping Rodgers and replacing him with another upstart will only take us a couple of years back. If he won't be replaced by a top manager, there's no point in sacking him.
By that logic, Man Utd shouldn't be in a position where it's possible that they could actually win the league (won't happen, but still).
Southampton should be mid-table with Koeman, take off the fact they sold Lallana, Lovren, Shaw and Lambert and they should be in a relegation battle which a lot of people predicted.
Spurs haven't dropped since Pocco took over and are still in a fight for top 5. West Brom have actually gotten better since Irvine took over.
Pardew has taken Palace from 18th to 11th.
The others haven't had long enough to judge yet, but are all where they were when their last managers left.
In other words, you're simply making up excuses. Just about all LFC managers have won something in their first season with the club, Rodgers is the only one for about 50 years who hasn't.