Tywin is no Aegon the Conqueror.
No one claimed he was. Just giving an in world example of how shit children does not mean ones legacy is made shit.
Robert's legacy is more than secure even if none of his 'children' have long successful reigns.
And Aegon very nearly did have his entire legacy go up in flames.
How so?
Luckily his family had dragons. And we should condemn Aegon for by raising up a worthy successor.
Why should we?
Historical legacies rarely work like that. Figures are based on their accomplishments in life not what their successors do.
Gerold the Golden has a very respectable legacy despite his heir being Tytos.
Tytos is regarded as a joke despite his children being successful.
Tywin will largely be judged on the four decades he was a huge influence on Westeros.
If you want we could even talk about real life. Henry V is no less of a success because his heir was a shit ruler who lost the Crown to the House of York.
What? I didn't say he was disappointed in the last 40 years.
You claimed he was 'building a glorious new Lannister era'.
Tywin wanted a continuation of the influence the Lannisters had the last 40 years, he was more than happy with the era.
I mean he does tell Jaime that he wants King Tommen to be taken to Casterly Rock squire for him and be taught to be a Lannister.
Yup. But not to change his last name. Ned wanted to Robin to come to Winterfell so he could teach him.
A Baratheon would still be King. Tywin was not trying to change that.
I believe Ned, Robert and Tywin were in their early 20's when they became Lord Paramounts. I might be wrong though.