The Supreme Court. Supposedly nonpolitical but in reality a political mess.
Yes, the justices need to have long terms to avoid the short term, short leash of political debts. But lifetime? NO! No one should have this kind of job/power for life. Give them a one-time term of 15 years – long enough to outlast any one president or even two, but more than enough for one person.
AND their confirmation has to require a minimum of 2/3 of the Senate. No simple plurality – too partisan for such a powerful job.