On the other hand, manager writing production code is a terrible footgun for the team. Time/resource conflict between helping a team and shipping code has no good outcome, either I let team down by decrease their productivity, or I let team down by slacking behind.
What I saw is that role isn't working either way. TLM don't have manager's power (can't reward and cannot punish) and at the same time expected to churn out production code, carving continuous focus hours out of manager's schedule.