We're conflating a lot of different professions here. Phlebotomists only have trade school, but they're still going to be exposed to some pure science - at the least biology but likely chemistry as well - in high school.
Nurses and especially Doctors have years of pure science before they're ever allowed into their trade schools.
Likewise there are a variety of software careers, from sysadmin to developer to architect that require varied levels of education (though much like nurses developers can only benefit from better understanding of the principles behind their art.)
>Nurses and especially Doctors have years of pure science before they're ever allowed into their trade schools.
This is an (unnnecessary) North American tick, whose pernicious influence is spreading.
Medicine has traditionally been an undergraduate degree in Europe and all former European colonies aside from the US, and those countries that are in its cultural sphere (like S. Korea, which got rid of its undergraduate medicine degrees.) My cousin started his Medicine degree at 17. It will take him five years. It's not like this is even unknown in the States, IIRC UCSD has a runaround where you get a Bachelor while doing an M.D.
And even in the US there are different types of nurses, some of whom went to college, some who didn't (LPN, RN and Nurse Practitioner). I understand demanding continuing education and testing to ensure competency, but college is a means of doing that, but not the only one.
And demand for doctors is kept artificially high via a small number of available med schools[1], incenting the profession to erect increasingly high barriers to becoming a doctor.
Nurses and especially Doctors have years of pure science before they're ever allowed into their trade schools.
Likewise there are a variety of software careers, from sysadmin to developer to architect that require varied levels of education (though much like nurses developers can only benefit from better understanding of the principles behind their art.)