**...Like at the Last Supper when the Eucharist was instituted :-)**
But at the Last Supper, Christ blessed the wine and gave it to his disciples also, (Eucharistic Prayer III):
"When supper was ended, he took the cup. Again he gave you thanks and praise, gave the cup to his disciples, and said: 'Take this, all of you, and drink from it. This is the cup of my blood, the blood of the new and everlasting covenant. It will be shed for you and foa all so that sins may be forgiven. Do this in memory of me.'"
You are right, that sounds like the best of both worlds.
It's called "intinction". When I was much younger, that practice was common on major feast days. In my Parish, anyway. I always liked it, although it required extra vigilance of me as an Altar Boy. Communion in the hand largely killed the practice. My current Pastor does it occasionally.
FWIW, it is the norm in the Eastern Catholic rites, and they use a little golden spoon to give Holy Communtion to the faithful.
Communion by intinction. In the Maronite Catholic Church (as well as the other Eastern Rite Churches), communion is by intinction. The priest (ONLY the priest or a deacon - there are no EEMs in the Eastern Churches), dips the consecrated host into the Precious Blood, and places it on the tongue of the communicant with the words: "Receive the Body and Blood of our Lord, Jesus Christ, for the remission of sin and eternal salvation."
For large gatherings, intinction sets are used to distribute communion under both species.