If you are receiving the consecrated host, it has become both Body and Blood, Soul and Divinity. If you are receiving from the chalice, you are receiving the Body and Blood, Soul and Divinity. So asking if somebody receives “the precious blood” is a little confusing. If you receive communion under either or both forms, you receive both Body and Blood.
Even though the OP knew exactly what he meant, IMO this shows that the church had a very good reason to want the people to receive only the host. Too many people are confused and think that they don’t ‘get it all’ if they don’t receive both. Even to call receiving both ‘a fuller experience’ is a little confusing, because you do not get more by doing so.
We do not have the same type of society as existed in the early church. We do not receive in our homes, we are not small groups of people, and culturally speaking, a lot of us don’t even know how to handle wine the way that a 1st century AD person in virtually any culture would have. So unless we take a great deal of care, there exists a lot of opportunity for abuse of the consecrated wine, both physically and obviously ‘intellectually’. I’m not saying it’s bad, and if it is offered in your parish and you like to receive, I’m all for you. . .but you are not ‘required to’.