NHS waiting lists.
Schools where being present when the register is called is given priority over missing lesson time if a pupil has a medical appointment for example.
I worked for a consultancy where internal cost structures meant it could be cheaper to outsource work to other companies (luckily it often just took a quick chat with a department head to show how ridiculous this was and to keep the work inhouse, so maybe not the best example).
I never had understood the logic behind a department being penalised if they didn’t use all their budget (not my company).