I read this in disbelief, picturing a uniformed INS employee drawing vials of blood in some poorly sanitized strip mall. It turns out US green card applicants are required to show proof of vaccinations and undergo a physical exam by performed by USCIS certified physician. For adults, the exam includes a blood test for syphilis. Source: https://www.uscis.gov/tools/find-a-civil-surgeon

Also a chest X-ray to check for TB, a lazy question to the crowd - could that not also be performed via blood test?

It's not that simple, Once you have been exposed to TB, you will always test positive. A chest X-ray is the only way to know if the TB is active or not(that I'm aware of currently). Source: I'm one of those that always test positive to TB tests.

Obviously, it's to prevent people with chronic medical conditions from pursuing citizenship so they can access free health ca- oh wait.