What exactly are people trying to argue here, that Klopp hasn't been one of the best managers ever in the league? It takes some level of bitterness or just idiocy to try and paint him as anything but that.
He lost the league on multiple occasions to complete cheats, he built the most entertaining team in the league, on less money than numerous others, and won the CL.
He's clearly among the best managers the league has seen, and is certainly among Liverpool's own list of great managers, but I think the general point is that it's a bit of a myth that he'd have cleaned up without City. He's finished second to them twice, which is the same number of times we've finished second to them in that timeframe.
His record is 8th, 4th, 4th, 2nd, 1st, 3rd, 2nd, 5th.
For context, Fergie didn't finish outside of the top two in the PL until 2001/02, and didn't finish outside of the top three at all. Wenger's record at Arsenal between 1996/97 (when he took over mid-season ,with them having finished 5th and 12th in the two years prior) and 2004/05 was 3rd, 1st, 2nd, 2nd, 2nd, 1st, 2nd, 1st, 2nd.
The situation with City has been a convenient mask for an obvious lack of consistency with Klopp. He followed up the title win by needing to claw his way back into a CL spot, after going on a run of 14 games and three months with just three league wins and eight defeats. Even then, it required Leicester to win just one of the final five, and Chelsea to lose two of their last three, and Alisson scoring a 96th minute winner against West Brom, for them to secure their spot in the top four. He followed a quadruple hunt with a season that saw them 6th and below for the entirety of the first half, and dropping as low as 10th in the second half, and ultimately culminated in them finishing 5th.