1. It's not like those math Ph.D.s are sitting around reading textbooks with their advisors.
They are TA'ing service courses. A lot of TA'ing. In addition to TA'ing, they are prepping for a high-stakes exam.
The exam will wash out the 50-70% of people who are needed as temp TA labor but whom the department has no intention of advising through to a Ph.D.
After 2 or 3 years, you pass the exam. Yay! But wait. Reading textbooks with your advisor? No! you need to take a whole slew of courses. Why? Because course enrollment == money and easy/interesting teaching assignments. And good luck getting tons of research done in-between your TA'ing and courses...
Now you're done with courses! Yay! After TA duties, you can spend 100% of your time on research (aka 50% of a 40 hour work week aka 80% of a grad student work week). Except you only have 2 years left :-(
So now it's on to 1-3 postdocs so that you can start doing, after 5 years, what that CS phd student was doing when they "hit the ground running": build a research agenda that resonates with a large enough set of researchers that it translates into a research job.
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Also, the "one singular result" style of research is unique not just to mathematics, but to a particular subset of mathematics. It's just not a good fit for most research problems, even in Mathematics. I've seen tons of well-composed dissertations focused on a singular, pointless problem.
The hodgepodge dissertations don't have a "beautiful singular result" feel, but almost invariably contribute at least one piece of useful, new knowledge.
Finally, worth noting that the best and brightest don't leave research; they might leave academia, but typically not research.
TL;DR: If you can find an advisor who isn't a slave driver (the majority of them at good places), the CS model is 1000% better than the Math model. You might be hired as a researcher for someone else's research agenda, but at least you don't spend the first 1/3rd of the phd as temp teaching labor stressing over high-stakes exams.