In the old days of the Middle Ages, the Sacred Blood was reserved for the priest, since spillage was always a concern; it would not be seemly for Christ's Blood to be trampled underfoot. In addition, there was always sanitary fears, since diseases from trench mouth to plague abounded. Coupled with this was the fact that the priest, all by himself, would be spending a lot of time distributing the Sacred Blood.
After Vatican II, when laypeople were instituted to be extraordinary ministers of the Eucharist, there was less concern about overworking the priest, since he now had plenty of help, and diseases are much less prevalent these days. (No one is required to receive the Blood, if they happent o be squeamish, however---or if they have a weakness for alcohol and wish to avoid it.) Ministers are also trained to avoid spillage, and if an accident does happen, they're trained how to handle it. (You place a pall over the spot to keep people from stepping on it, and you clean up the spill after Mass.)
In the United States, we have received both Species since Vatican II, under an indult from the Holy See; this was not the case with much of the rest of the world. However, I am happy to report that with the issuance of the revised Roman Missal within the last couple of months, the norms have been expanded to include the entire world---so you will probably be seeing Communion under both Species everywhere very soon.