As to why unemployment is such an important figure: it speaks to the economic security of the main mass of people. Most people don't believe they will ever be disabled. It's all too easy for them to imagine being unemployed.
What may operate as camouflage for long-term unemployment in the statistics is a medical decision the person is unfit for work. (For psychological reasons, for example, or chronic backache, etc). This may not be a lifelong decision, and will probably be subject to regular re-appraisal. But it takes an unemployed person off the unemployment statistics and on to another set that is not given public prominence...