I don't think there is any one factor, though I'm surprised by the impression I'm getting from your post of extreme variation in your field; I'm mostly familiar with extreme variation in teaching expectations between fields plus variation on a student-to-student basis, based on funding available to them individually.

Some programs value teaching experience. They may see failing to provide teaching experience for PhD students as failing to produce well-rounded PhD graduates. Training faculty with research money may even find this irritating if they want their students to work on their grants and have the funding to support them yet the graduate program requires students to teach anyways.

Other programs may support their students almost entirely by teaching, and recruit exactly as many students into their program as are needed to fill those teaching slots. Unless the program is certain a student with funding can support themselves for the entirety of their stay so that they can open up a new slot and take on a new student who will fulfill those teaching responsibilities, they need everyone to teach.

Otherwise, I think it's mostly up to the funding available to each individual student. That may mean that the type of funding depends far less on the graduate program and far more on the student's specific research interests or mentor. Some mentors may be well-funded and able to support their students more directly; perhaps they have a rare source of funding in a field that doesn't normally have a lot of extramural money. Perhaps they have a more applied area of research that attracts industry or other types of money.

Students looking at graduate programs should expect the programs to provide information on funding: what sorts of arrangements are likely, what is possible, how are current students funded on average, etc. - I do not think there is any quick way to get around needing to collect this information for a program that you're anticipating spending several important years at.

I don't think there is any one factor, though I'm surprised by the impression I'm getting from your post of extreme variation in your field; I'm mostly familiar with extreme variation in teaching expectations between fields plus variation on a student-to-student basis, based on funding available to them individually.

Some programs value teaching experience. They may see failing to provide teaching experience for PhD students as failing to produce well-rounded PhD graduates. Training faculty with research money may even find this irritating if they want their students to work on their grants and have the funding to support them yet the graduate program requires students to teach anyways.

Other programs may support their students almost entirely by teaching, and recruit exactly as many students into their program as are needed to fill those teaching slots. Unless the program is certain a student with funding can support themselves for the entirety of their stay so that they can open up a new slot and take on a new student who will fulfill those teaching responsibilities, they need everyone to teach.

Otherwise, I think it's mostly up to the funding available to each individual student. That may mean that the type of funding depends far less on the graduate program and far more on the student's specific research interests or mentor. Some mentors may be well-funded and able to support their students more directly; perhaps they have a rare source of funding in a field that doesn't normally have a lot of extramural money. Perhaps they have a more applied area of research that attracts industry or other types of money. Perhaps the student has applied for and received funding through a fellowship that funds the student directly; these opportunities are relatively rare and a student that receives one may have an entirely different experience than anyone else in their program.

Students looking at graduate programs should expect the programs to provide information on funding: what sorts of arrangements are likely, what is possible, how are current students funded on average, etc. - I do not think there is any quick way to get around needing to collect this information for a program that you're anticipating spending several important years at.