I can imagine that the series is written from a staring point, then with the final outcome envisioned and then with the backstory filled in to dedevelop character and provide motivations.
More than enough is shown of Tywin’s deviousness, callousness, greed, ruthlessness, and brutality. The complexity is delivered by showing that his “managerial” skills are mostly successful during turmoil, promoting his house, or to shut down dissent. He displays clever Macheivellian techniques without heart. So if you are a fan of brutal, but pragmatic authority, then he’s your guy. If you value family relationships, then he is a disaster, except that he did try to protect Genna, although it might not have been for heart reasons. (Perhaps status reasons) His relationship with Johanna is really unknown on her part. Perhaps the lady didn’t like him as much as he would have liked.
The Greyjoy survival might have been because they were needed in the series down the road, or maybe even because Martin was really keen on showing us a Viking style culture, a tortured Viking/Nedified conflict character in Theon that could reflect the real world change in Scandinavian culture, or possibly to provide Dany with a fleet for invasion. Only the author knows for sure!
Other people have pointed out that Martin shows what his judgment of Tywins character is by his death details, and the chaos in his children’s personal lives. And he does it all stone cold sober.