Why transcripts instead of degree certificates?

Most applicants for positions at US universities will have been educated in the US, so US hiring practices are based around the sorts of records that US universities provide. And US universities don't really have such a thing as "degree certificates". The paper diploma from a US university is considered purely ceremonial and not used for any official purpose; it often doesn't even have complete information about the degree (major, honors, etc). For most US universities, the only official academic record they produce is the transcript. Hence, that is what a US university expects when hiring.

Note that in some cases, a hiring decision may be based on more specific details about your education than the simple fact that you have a degree. There may be formal requirements, coming from university regulations or accrediting agencies, that you have a certain amount of coursework in certain areas, and the transcript is the only way to verify that.

At the heart, the approach chosen by universities is because a piece of paper, however elaborate, can be forged. It is much more difficult to forge the transmission from one university's degree verification office to another university. So in some sense, the request is simply to make forgeries harder.

It's not part of your question, but worth telling stories around it. The kind of requirement you are encountering makes it much more difficult for people from other countries to satisfy the formal requirements. I have colleagues who were professors for 20 years and, when accepting a position somewhere else, where asked to provide a way for the new university to verify their PhD -- which they had obtained in the 1980s in Eastern European countries that no longer exist, at universities that no longer exist and whose archives were affected by years of civil war. I don't recall how that was eventually resolved, but it seems unlikely that the new employer ever got what they were asking for.

Accreditation to teach specific classes.

For example, the college I work at is covered by SACS. With just an AS degree and a metric ton of experience, I can teach IT courses that don't count towards a BA/BS degree at a "real" University. Linux administration, Advanced Java (but not intro to programming w/ java), MySQL, etc. They qualify for vocational certs and AS degrees though.

In order to be able to teach specific courses - IE, "CGS1000" titled as "Intro to college computing" which DOES go towards AAs and 4 year+ universities, I have to either have a masters or terminal degree in a specific named field, or have X number of hourse (18 IIRC) of post-grad course work in a specific list of courses. It is that last bit that requires a transcript, and it requires someone to evaluate the transcript, compare substitution codes by FICE codes (to see that your schools ABC123 mapped to what SACS calls ABC101), etc.

A good example of this is someone I work with who has a BS in software engineering and a masters in project management but he can't teach the CGS1000 course because he didn't have any educational technology related courses at the masters level.

Edit - explanation of terms

SACS - Southern Association of Colleges and Schools. Accreditation body for SE USA.

AS - Associates of Science degree. 2 year terminal degree (nursing, X-Ray tech, Resp. therapy, etc). Minimal gen-ed stuff, doesn't go to a University to become part of a higher degree

AA - Associate of Arts. First half of a BA or BS degree, gened type stuff.

FICE - Federal Interagency Committee on Education - defines a nationwide list of code numbers to reference schools and/or courses for cross-institution communication of academic info like transcripts, etc.