I like the idea, but I'm not sure that the savings would be worth the costs. The difficulty is that it is very hard to match the time of the accident to the cell phone records. The car's event recorder is not accurately time synchronized. The cost of equipping event recorders with time synch for gathering accident/cell relationships is too high for just research. If there was some significant monetary value, that could change this. But it needs to be more than just a change in fault assignment because insurers cover both sides.

For example, I've always liked the idea of enforcing seat belt laws with a mandatory $10K extra deductable on health payments for the person not wearing the seat belt. They get to pay some of the extra costs resulting from their decision not to wear a seatbelt. This is probably not all the extra costs, but if the level is too draconian the public will not accept a change like this. The insurers would become interested in cell records if there was an extra deductible paid by the driver in the event that they were contributing to the accident by talking on the phone at the time. Then there might be enough incentive.

As for your concerns on anonymous data, I routinely see effective anonymization. The problem is not technologies. The problem is taking the proper approach. Most people want to gather and mine a vast pool of anonymous data. That does not work. That is relatively easy to break. Good anonymization starts by determining what is the minimum data that must be collected to answer the question being asked, and removing everything else. This is the approach typically used in clinical drug trials, where the requirements for effective double blind analysis coincide well with the needs of anonymization. Breaking the anonymization of drug trial information cannot be done by a simple flip the switch. It takes several steps.

The clinical trials also design in a simple method for breaking anonymization when appropriate, which reduces the pressure to defeat the anonymization. If a trial investigator happens to notice an unrelated disease indication, there is an established series of trusted third parties, none of whom have complete knowledge, for getting a notification back to the correct patient and their doctor. There is less pressure to gather excess data because this does not benefit the drug sponsor, investigators, patients, or regulators. So privacy violations tend to be accidental, misunderstandings of procedures, or mistakes in determining the minimum data requirements for the study.

I'm not sure there's any controversy about this at all amongst the scientific community. Drivers on cell phones have been reliably associated with car accidents, and there's a fair bit of evidence that using a hands-free device doesn't help, which suggests that the challenge is attentional, not manual.

The intellectual challenge of scientific research is to come up with experimental designs that allow you to test hypotheses while minimizing expense, time, and risk to the participants. Researchers have come up with several ways of measuring the risk of cell phone distractions to drivers. A quick look at Google Scholar gets you papers on driving safety and cell phones from the Journal of Experimental Psychology: Applied (Strayer, Drews & Johnstone, 2003), another from Accident Analysis & Prevention (Matthews, Legg & Charlton, 2003), Human Factors (Strayer & Drews, 2004) and a piece that comes closest to answering your question directly, in BMJ [British Medical Journal]:

Role of mobile phones in motor vehicle crashes resulting in hospital attendance: a case-crossover study (McEvoy, Stevenson, McCartt, Woodward, Haworth, Palamara & Circarelli, 2005).

The findings are available at http://www.bmj.com/cgi/content/abstract/331/7514/428, but I can summarize here. They looked at 456 drivers who owned or used cell phones and had been injured in accidents seriously enough to require a hospital visit. Researchers checked to see who used their cell phone within ten minutes before their accident, and compared that to their cell phone use around trips at the same time of day in the previous week. "Driver's use of a mobile phone up to 10 minutes before a crash was associated with a fourfold increased likelihood of crashing (odds ratio 4.1, 95% confidence interval 2.2 to 7.7, P < 0.001)." Or, as the researchers concluded, "When drivers use a mobile phone there is an increased likelihood of a crash resulting in injury. Using a hands-free phone is not any safer."

A fourfold increase in the risk of crashing, with a P < 0.001, is weighty evidence.

As Linda pointed out, there is little value in doing this study, but I'll explain why it is a bit more anonymous than you think. First, the database is spread across multiple vendors, never all in one place. Second, it is transient. Data can be discarded after a month or two. Third, it needs only track a location history, with no relationship to any subscriber identification. There is still a privacy risk, but not much greater than the existing privacy risk. Assuming that it can be done at all (which I still question), this has the organizational benefit that it would be policy to not collect identifying information when gathering location. At present, the policy is open.

I do have doubts about it's feasibility. Most of the electronics that I have seen uses RAKE transceivers. These do not internally track distance or angle information. They only track phase shift and frequency shift correlation numbers. The correlation numbers need never leave the transceiver. Pulling this numbers out to get more detailed information than cell tower is not fast or easy. They are rapidly changing, and converting them into angle and distance is subject to a lot of ambiguity. I could see it being reasonable if I had already identified a particular target to track,e.g., e911, but not as a general practice. Easiest is tapping into GPS equiped cell phones.