TOTD - judging by the poor girl's injuries, it would have made little difference in this case.
We have had situations in Wales where only a police officer can request a SAR helicopter (their rules not ours) whereas an MRT cannot. It all comes down to training and liaison.
Turkey - it comes down to cost, both for the winch and the training required to keep competent at winching ops - since the AAs in UK are funded by charity and only a few areas in UK would be likely to use the capability, it hasn't happened. There have also been questions raised about aircraft performance during winching.