I have found a significant amount of research being done on the topic and one of these papers may contain the answer. Here is a list of some further resources, all relatively recent, all regarding exhaust-driven air conditioners:
Some of those papers, while published, are a little disappointing, but there are a lot of others, check out this google search.
Most of the designs seem to be based on the principles of a Brayton Cycle engine, operating in reverse.
As for why they are not prevalent, an interesting tidbit from that reverse Brayton cycle link, which could be a hint:
As can be seen, the cycle efficiency is not very high (0.85), but the system is relatively simple, and has moreover the advantage of not releasing any greenhouse gases in the event of accidental breakage of pipes.
Air reverse Brayton cycle was until recently widely used in aircraft for in flight cabin air conditioning.
Note that I do not know why aircraft no longer use that cooling method, research into that could also lead to related material.
But the most interesting quote is from the first paper above:
For a typical small-size car with a maximum
engine power of 51 kW, turbocompressor impact on
the engine is 1,7 kW, which is similar to the typical
compressor power consumption of a conventional air
conditioning system (about 1,6-1,7 kW according to
Kaynakli & Horuz, 2003).
Another aspect to be considered in terms of
engine impact is the system weight. The weight of the
proposed system was evaluated to be about 11,5 kg,
while the conventional system weighs approximately
Taking these aspects into account, this first
approach indicates that the proposed system would
increase fuel consumption, mainly due to higher
weight. Nevertheless, considering that system
weights are very similar, an optimizing process on
proposed system might eliminate such fuel
Which basically states that, at least in that initial design, power consumption was actually similar but weight was increased, and so there was no net improvement over a traditional A/C unit.
Given the date of that paper (2009) and the fact that research is ongoing, it is not unreasonable to imagine improvements have been made (I admit to not having gone over the other papers in detail), but I am presuming that not enough improvements have been made to make a change compelling.
Note: This is assuming that these papers are actually related to what you're describing -- these are turbo-driven systems in that they run off exhaust gas, but have a dedicated turbine, rather than running off the turbine shaft of a turbocharger, although at the end of the day it's essentially the same as far as energy transfer goes, I suppose, and for some of these designs the A/C still needs it's own compressor-side turbine regardless of what's on the other end of the shaft. A lot of these designs do seem to use different refrigerants than common typical A/C's, though.