I have no idea whatsoever the thinking on that. The more we see though, the ore it feels like a power play between Klopp and the owners. You get that a lot in businesses, that arguments are conducted via essentially totems. That is what I sense Thiago was, a Power play from the manager to get them to break with all of their previous protocols and back him. When you do that, and it goes as spectacularly wrong as it has done, you really weaken your position. I'm pretty sure there current run of 2 wins in 11 (I'm not going to count their win against Aston Villa's children as a win,as the following day Chorley FC beat a youth team) has culminated with his return to the team hasn't it?
This may not follow the common consensus that's currently being mentioned, but I don't think Thiago is a bad player - in fact, he's previously shown otherwise.
Whether he's currently out of form or not is a question which I can't answer, however I'm pretty certain that he doesn't fit the profile of the midfielder they need.
For years now, they've played quick football and their midfielders have been expected to move around, press, cover and move the ball quickly to wing or up front.
Thiago simply doesn't do that and as such his deficiencies come to the fore: in the system they play, he looks very poor and he probably limits their overall play.
Perhaps Klopp was signing him in mind of potentially adapting their style of play or at least having different options, but the way I see it is he's been shoehorned in.
That's not to say they should make wholesale changes to suit him (God, I'm loving their current style!), but why buy him if he doesn't suit the style you wish to play?
Maybe the original reasoning behind purchasing him was sound, yet Klopp's inflexibility has meant that he's been given a raw deal and making the RS play worse.
It reminds me a little of Kanté at Chelsea, who was terrific at Leicester and initially at Chelsea too; he was then told to another job and low-behold he looks poor.