I work for an insurance company.
Sometimes insurance claims can be filed weeks, months, or years after the original injury occurred or after medical treatment was sought (in the case of lawsuits, years are not uncommon). In which case it is handy to know the age at the time of injury, which does not necessarily coincide with the claimant’s current age. A computer can technically compute this, of course. But I also know that when we’re taking different types of claims we ask for different kinds of information. If you slip and fall at a business as a customer, and they file a general liability claim about what happened, we would ask for your age. If you slip and fall at work on the clock, we would ask for your date of birth (and the system visually calculates the age of employee on the date of injury). I’m not 100% sure why the difference exists, but there you go.