Tyrell Wellick from Mr. Robot already had everything that he might have wanted — a good house, a limo, a kinky wife, and was soon to be a father — so what was the reason he became CTO? People work to attain something whether it’s money or just because of passion, but Tyrell already had money and the CTO post is nothing more than a title, nothing to be passionate about, so why did he want it?
This answer deals with some of seasons 2, 3, and 4, so if you haven't seen it yet you may want to skip over. The biggest spoilers are in spoiler tags.
There was a quote that Phillip Price, the CEO of E Corp said
In my life, as I was making my way, I always asked the question, 'Am I the most powerful person in the room?' And the answer needed to be 'Yes'. To this day, I still ask that question.
That is because he is a man of ambition. He had to achieve and gain more and more power until he was the most powerful man in the world. It wasn't about money or titles. It was about power.
Likewise, Tyrell Wellick is a man of ambition. He grinded his way up the food chain to be as successful as he could be. He was a very powerful executive in E Corp even before being considered for CTO.
This ambition is also evident when:
he became CTO. Phillip told him that the position would be ceremonial and would hold no real power. Tyrell would just be a figurehead. There was a serious look of disappointment and anguish in his face when he found out the post held no real power. It wasn't what he wanted.
This also is shown when:
He starts working with Elliot. He took his work with Elliot very seriously. To him, the work they were doing was making them gods. He even said as much. You can't really get much more powerful than a god.