Just theorising....is it because his brand of football is not sustainable long term? Maybe the pace/high level intensity catches up with the players in the end so he thought that Thiago would help keep the ball when winning, slow the pace down and ride out the game
What you say is most likelytrue and there could be many things that effects Klopps football.
His game rides on a squad arguably mostly in their prime working in a team sync of hard work and pressing. Liverpool at their best arguably creates chances/pressure from their pressing ability more or just as much as their other attacking abilities like their fullbacks (which also arise from the opposition being pressed and the ball getting recycled to the fullbacks etc).
Then you look at someone like Firmino who did considerably well under Klopp but is a little less consistent now a days (I wouldnt say he is useless like some do). This could be due to Firmino feeling lethargic or instead Liverpool needing that change of tactic after playing the same formation or tactics for a long time.
Consider Jota for example, many thought he was going to be a back up for Mane but ended up playing as a CF instead of Firmino. That tactic which had worked for 3 years is not as good as it can be right now and a CF is required. Whilst Jota will more likely score more goals - there is a slight possibility that alternative tactics effects Mane and Salah by 5% (arguably their main forwards of the last couple years) whilst we see Jota being the most dangerous forward of the lot.
It's just an example but ultimately it can be seen in midfield too - the midfield balance and type that worked (Fabinho, Henderson, wijnaldum, Chamberlain, Keita, Milner etc) is being changed a bit to accommodate Thiago who plays football in the most different way out of the lot. Thiago will bring his benefits to Liverpool but he will also remove some of the strengths the team already had previously. Say its Milner or Wijnaldum that gets stuck out for Thiago - liverpool get a different tempo to their game overall related to their attacking ability as well as their defensive ability. Suddenly they arguably have a creator in the middle making chances when the whole team was successful arguably pressing and not relying on such a creator at all.
The one last minor thing to add to the list is that their is not much rotation happening either which also adds to fitness problems. I also personally feel that Klopp's players get a bit big headed after feeling that they have achieved the max at their club to the point that they consider a change alongside the possibility that Klopp might feel the same underneath ( Lewandowski, Sahin, Kagawa, Gotze at Dortmund and you hear players like Salah, Widnajldum wanting to leave too.) This also leads to a need of change and targeting different players to freshen things up at the core.
All of this has to kind of combine because all managers need to change their tactic eventually (we never saw Cole and Yorke be the sole tactic of SAF's tenure but we saw him change it up and use Ronaldo, tevez and rooney just as much as he used Van Nistelrooy by himself) - it just feels that Klopp's tactic A is slightly better than his tactic B, that's why he jumps in and uses it at the start of his time at the club but ends up changing it when it has to be done.