I'm not certain that my experience is still completely valid as it was very long ago that I entered graduate school in math. I'm now retired and have been for several years. But I'm pretty certain that I wouldn't have earned a doctorate under a different system.
I entered an R1 program in the mid 1960's with a full fellowship. It had the requirement that I spend one year as a TA, to get some teaching experience. This fellowship program was part of the push by the US to beat the Soviet Union to the moon. It no longer exists.
I made relatively little progress, other than coursework, during four years and left with a masters for another R1 where I completed the PhD. Before I discuss the latter program, let me give a few reasons why a fellowship without teaching duties doesn't make it quicker or easer to get a degree. I was limited by a few things. The low income from the fellowship wasn't one of them, and I was one of the few to hold one. I had an advisor who wasn't sufficiently helpful as he was, at the time, up for tenure and worried more about his future than mine. I also didn't yet have the required insight into the deep nature of mathematics, though I was pretty good at solving problems and passing courses (high GPA). It turns out that in most research (I think) but especially in mathematics, more time in the office doesn't equal more insight or more progress. Getting that insight requires "seasoning" and it can't be scheduled. I had few duties, other than making progress toward the degree, but made little progress. No more than my peers who were TA's. I think it might have been different if I'd had the courage to switch to another advisor, but my basic introversion (worse then than now) made that impossible for me to do.
Eventually, after getting a bit burned out, I switched to another university and had a TA position and completed the degree in three years. I had a better advisor and conquered the burnout, but made better progress even though I had teaching duties. I also gained better insight into a small area of math and became, in the words of my advisor, "the most knowledgeable person in the world in ..." (paraphrase).
But, also, let me say some things about that second university. It was, like the first, a large US State university. As such it was partly supported by tax revenues, as well as grant funding from various places. The student tuition, at the time, was fairly low, and it was not paid by TAs. The stipend we got was very low - about the same as the fellowship I'd had earlier, but there were few expenses and I was able to graduate with a family, supporting them from the TA income.
The math department at the second place had about 60 full time regular faculty and about 180 full time grad students, almost all of which were TAs. The TAs normally helped a professor in a course for a year or so and "graduated" to teaching our own courses, say in calculus. But the system as a whole wouldn't have worked any other way. If those grad students were replaced with regular faculty (doubling the size of the regular faculty), if you extrapolate that to the whole university (about 40,000 students), there wouldn't be room for everyone, either in office space or in housing in the local area. Moreover, the students would need some sort of funding. If they had to rely on outside funding it would have been impossible to support even a small fraction of them in the local economy. Funding them with grants or stipends without work would have been infeasible as the governments had no interest in expanding to such an extent, nor could the grant funding agencies taken up the slack to such an extent. And the commitment of state governments to supply funding has only gotten worse in recent years in many places. This has been supplanted by increases in tuition fees, mostly paid by undergraduates and funded through a loan system that has many issues of its own.
So, working as a TA did many things. It gave me a small, but adequate, stipend, without which I'd have no place in academia. It gave me a bit of teaching experience, which also helped me learn how people learn (and don't). But it also gave me time. If it stretched out my education by a bit, that extra time allowed me to get the seasoning and insight that I probably wouldn't have achieved if I'd been on a more intensive "research only" regimen. As I said earlier, insight can't be scheduled. It takes time and reflection. It takes time away from the desk. So the time spent teaching and grading was just a break in the intense research that let ideas settle and integrate themselves into my thinking.
So, IMO, graduate schools don't use TAs because it is the expedient thing to do, but because it is a good thing to do. Give students a broad view of academia, even from the R1 standpoint, and the time in which to gain a bit of sophistication in their field. The low pay isn't such a terrible tradeoff unless money is your main driver. It isn't for most academics, I suspect.