Indeed. Often mutually exclusive.

To really build great software, you need time and space to git your head around the problem. This is obviously not possible if you're spending most of your week in meetings and tracking the work of 7 or 8 team members.

In my experience, you can be a great IC *or* a great tech lead, but you cannot be both at the same time.

A person might very well be suited for both IC or team lead, there is no conflict in the skills themselves. But as you say, actually trying to apply them both simultaneously in practice could lead to conflicts.