There are a variety of industries where it is a legal requirement to be of a certain age, either directly such as applicable law specifically states or indirectly such as a need to obtain age-restricted certification or use age-restricted rights.
In these cases, proof of birthdate as proof of legal age is a necessary part of demonstrating qualification for the role (indeed, sometimes it is the only qualification). Various terms exist to describe the broader category of genuine occupational qualifications and they are a defence against age discrimination in most sensible labour laws.
Birthdate is also often critical information for financial and criminal background checks, which are also legitimate uses of personal identifying information in the context of employment applications, and an employer may rightfully reject (or decline to consider at all) an applicant who cannot provide the information in a verifiable way.
This is also why you must provide a notarised acknowledgement of the identity document. Checking the ID themselves means they need you to be there with it! This is obviously a major cost and a major risk for everybody concerned, if you are in another country, and simply isn't worth the effort. A notarised letter is simple and quick and cheap, carries zero risk for the company and provides a record for future reference if needed.