By my personal experience, I have found that the more you have to manage up and across the less the amounts of PullRequests. Yes, you want to stay on top on the Code, the quality the architecture the decisions and direction, you will be able to influence but you will not be able to contribute as much as you will like. And to be honest, a Manager and more a CTO are roles to protect the developers, to guide them, inspire them and allow them to do the best job possible while you deal with the politics, budgets, timelines, keep expectations healthy, deal with the situations of perceived low quality, negotiate features and times makes sure the team is not developing something that makes no sense just because someone things is a good idea while keeping an eye to the trends in the industry and see how that can be beneficial in the long term and how to get time and budget to allow the team to experiment and learn from it.
To be honest, try to do all of that and do it well and in a way that helps the team and you will find your self with no much time for code. This doesn't mean that you should not be able to roll your sleeves and code on a crunch time or be able to fire up the IDE and look for that piece of code that introduced the bug and fixed when is an emergency, you have to do it and do it well or at least in a helpful way.
CTO's are exceptions and they can still be able to code, but they need to have a team of Directors and Managers that will do their job well so will free his hands and allow him to work on some experimental projects that will provide future directions, but again it depends how much they have to manage up and sideways and the support from the staff below him.
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By my personal experience, I have found that the more you have to manage up and across the less the amounts of PullRequests. Yes, you want to stay on top on the Code, the quality the architecture the decisions and direction, you will be able to influence but you will not be able to contribute as much as you will like. And to be honest, a Manager and more a CTO are roles to protect the developers, to guide them, inspire them and allow them to do the best job possible while you deal with the politics, budgets, timelines, keep expectations healthy, deal with the situations of perceived low quality, negotiate features and times makes sure the team is not developing something that makes no sense just because someone things is a good idea while keeping an eye to the trends in the industry and see how that can be beneficial in the long term and how to get time and budget to allow the team to experiment and learn from it.
To be honest, try to do all of that and do it well and in a way that helps the team and you will find your self with no much time for code. This doesn't mean that you should not be able to roll your sleeves and code on a crunch time or be able to fire up the IDE and look for that piece of code that introduced the bug and fixed when is an emergency, you have to do it and do it well or at least in a helpful way.
CTO's are exceptions and they can still be able to code, but they need to have a team of Directors and Managers that will do their job well so will free his hands and allow him to work on some experimental projects that will provide future directions, but again it depends how much they have to manage up and sideways and the support from the staff below him.