LvG literally stumbled on that winning run due to injuries. But he ripped it apart and threw it out the window for the next season, which led to his downfall.
In a way, I get you. Jose should have kept some of the positives from LvG's tenure, like the focus on possession, and added his own signature of a solid defense to it. As an example, look at what Ancelotti is doing with Napoli. Their current style is still heavily Sarri-ball with a few characteristic tweaks.
Jose however, not only failed to capitalise on the possession play the players learned in 2 years, but he also tried to eke out a compromise between his own defensive style and the all out attack that our club expected in his first season. End result was a mess, so he reverted to over-cautiousness since the Anfield game last season. Even what he's doing now has no identity, but is more relying on the good form of Martial and Pogba, two players who don't really like his methods.
That is easier said than done when the coaches are from in-congruent schools of thought on how the game should be played.
Mourinho (and Klopp also) would rather develop an attack as quickly as possible, with pace and directness, hoping to get an opportunity before the defence settles in, while LvG, pep and the total football school in general, opt for a 'boa constrictor' approach of dominate possession enough and the opposition will crack eventually. Total football proponents prefer to maintain possession than make a mid probability attempt on goal.
The problem we have is a consequence of following LvG with Mourinho, has most of the players suited to one approach will be unfit in the other.
Mourinho would have had an easier task if he had a more generic squad or if not fully suited to his style, needing less changes to get a squad suitable to playing like he wants or the unlimited amount of money to overhaul in short period (like he did at Chelsea at first stint and Inter).
Mourinho's ideal squad probably consists of
- GK that can kick long with accuracy (like Cech),
- CF that can hold up and link play, preferably dominant in the air
- fast pace and high work rate full backs and wingers
- athletic CBs capable of playing a high line to shorten the field (e.g. Pepe+Ramos)
- destroyer DM that shields his defence
- enough height in team for dead balls
If Mourinho goes, it would be better to establish a philosophy and only hire coaches in-line with it, otherwise we might need another squad overhaul and/or have the inherited squad hinder the new manager