I learned that some managers punish their team leaders if their IC contributions are lower, instead of punishing them if their team management is lagging. This does not make sense to me. You are having a TL to help you make the team more efficient and to do that, the TL needs to invest time into it. Coaching and mentoring instead of doing the hard stuff himself.
I consider TL to be an IC, but they should be promoted if they have helped their team to deliver hard stuff and projects. Teaching them to do it themselves, helping resolve blockers and issues, not doing all the hard work as TL and neglect their team members.
TL needs to have the hard skill, but they do not have to use them all the time themselves. They need to transfer them to others, that is the purpose.